Non Calculator Tests

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Non Calculator Tests

• Fourth Year

2
Click on a number in the table above to go to the
test of your choice.
The solutions follow after the test
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Non Calculator Test 1
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Non Calculator Test 2

• 1. Find 8 of 24
• Evaluate ½ of ( 12¼ - 5¾)
• 3. If a 5 , b -3 and c 4 find the value of
  b2 4ac
• Evaluate 2.9 3.1 ? 2
• 5. Factorise 9x2 25
• 6. Solve 5(2x-1) 7
• 7. The perimeter is 32 , find x
• 8. Solve 2x2 98
• If 5 of a number is 12 , find the number.
• 10. Solve the equations x y 13
  
• x y
  4

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Non Calculator- Test 3

• Evaluate
• 2. Evaluate 21.6 3.2 2.1
• Find of ( )
• 4. Write ?60 as a surd in its simplest form.
• 5. Factorise fully 2x3 8x
• Simplify
• 7. Solve 5x 2(3x-1) gt 4
• 8. Remove the brackets (2x 3)(x2 x 3)
• 9. If sinA ¾ and A is an acute angle , find
  the exact
• value of cosA.
• 10. If y varies directly as the cube of x and
  x is doubled ,
• find the effect on y ?

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Non Calculator- Test 4

• 1. If f(x) 3 2x2 , find the value of f(-2)
• 2. Solve the equation 4x2 7x 0
• 3. Factorise fully x3 4x
• 4 . Simplify ?45 ?20
• Simplify the expression
• 6. The perimeter of a rectangle is 36 and the
• length is twice the breadth.
• Find the area of the rectangle.
• Solve
• Find 3 of 480
• 9. Evaluate ?2
• 10. Evaluate

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Non Calculator- Test 5
1. Find 25 of 19 2. If x -2 and y 5 find
the value of 3.
If the diameter of the larger circle is
20cm and the diameter of the
smaller circle is 10cm , find the shaded area.
Take as 3. 4.
Subtract 6.38 from 13.9 5. How many pencils
costing 14p each can you buy for 5 ? 6.
Change to a decimal. 7. A pupil scored
in an English exam. What was his percentage
mark. 8. Find the gradient of the line 2xy5
0 9. If y varies inversely as x and y5 when x
2 find a formula connecting x and y. Find
y when x 20. 10. If y mx c , change the
subject of the formula to m.
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Non Calculator Test 6

• If tanx find the exact value of cosx.
• Write the fraction with a rational
  denominator in its simplest
• possible form.
• Find 5 of 42
• Evaluate of
• 5. A rectangle has a length 3?2 and a breadth
  3-?2 .
• Find an expression for the area in its
  simplest form.
• 6. Factorize 6x2 13x 6
• 7. The perimeter of a square is 6cm. Find the
  area.
• If x 4 and y 25 , find the value of
• If f(x) 3x 5 and f(t) 32 find the value of
  t
• 10. Solve the equation 3x2 5x

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Non Calculator Test 7

• Simplify
• Simplify
• Solve the equation 5 2(2x 3) 13
• If T , change the subject of
  the formula to P
• 5. If x 4 and y 25 find the value of 2
• 6. If x y 17 and x y 4 , find the
  value of y.
• 7. If f(x) 5x 4 and f(t) 11, find t.
• 8. Simplify ? 60 ? 135
• If A is an acute angle and sinA , find
  the exact value of tanA.
• 10. Solve the equation 2x2 2x 0
• 11. The diagram shows the graph of the function
  y x2 4x.
• Find the coordinates of point P
• 12. Find the equation of the straight line shown.

.
P
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Non Calculator Test 8

• Simplify
• Find x as a surd in its simplest form.
• 3. If f(x) 1 2x x2 , find the value of
  f(-1).
• 4. If a -3 , b -2 and c 5 find the value
  of b2 4ac.
• 5. The gradient of the line joining the points
  (2,5) and (5,t) is 3.
• Find the value of t.
• 6. Find the coordinates of point T shown in the
  diagram
• 7. If x 2? 3 and y 3? 2 find the value of
  x2y2
• The graph shows the relation ? y varies inversely
• as x . Find the equation connecting x and y.
• 9. If y varies directly as the cube of
• x and x is doubled, find the effect on y.
• Solve the equations 3x 2y 3
• y 2x
  9

.
(3,10)
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Non Calculator- Test 9

• 1. What is the equation of the function shown in
  the diagram?
• 2. Factorize fully 15x2 x 6
• 3. If x -4 , y 2 and t -3 find the value
  of yt 2x2
• 4. Simplify ? 50 - ? 18
• 5. Simplify
• Evaluate
• 7. If y varies directly as the square of x and x
  is multiplied by a factor of 3
• find the effect on y.
• Find the equation of the straight line shown.
• Write x as a surd in its simplest form.
• 10. Write as a single fraction
• If , change the subject to
  T and hence find T when P 40.

4
180
360
-4
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Non Calculator- Test 10

• 1 Find the equation of the straight line shown
  in the diagram.
• 2. If x -2 find the value of 2x3.
• 3. Solve the equation 3x2 9x 0.
• 4. y varies inversely as the square of x and y
  1 when x 2.
• Find a formula connecting x and y. Find y when x
  4.
• Evaluate
• 6. Simplify ? 75 - ? 48
• 7. The perimeter of the rectangle shown is 62cm.
  
• Make an equation and find x correct to 1 decimal
  place.

Continued on next slide
23

• Simplify
• 9. Find 4 of 48
• Multiply out the brackets (2x 1)3
• Write with a rational denominator
• 12. Simplify the expression

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Non Calculator - Test 11

• Write down the equation of the trig. function
  shown in the diagram.
• If A is an acute angle and sinA ,
• find the exact value of cosA giving
• your answer as a surd with a rational
  denominator.
• Simplify the fraction
• Find the exact value of cosA
• 5. Remove the brackets (5-3x)(6-4x)
• 6. If x 36 and y 9 find the exact value of

360º
26

• Find x if 5x 2y 17 and 3x 2y 7.
• Find the gradient of the line shown in the
  diagram.
• Simplify the expression shown
• Find 25 of 47
• 11. Evaluate
• 12. If f(x) and f(t)
  , find t.

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Non Calculator Test 12

• 1. Identify the trig. graph shown in the diagram
• 2. Factorize fully 8x2 2y2
• If x -10 and y -4 find the exact value of
  giving your answer
• as an improper fraction in its simplest form.
• 4. Write as a single fraction
• 5. Evaluate
• 6. If f(x) 1 - 2x - 4x2 , find the value of
  f(-3).

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• 7. The area of a square is 300cm2.
• Find the perimeter giving your answer as a surd
  in its simplest form.
• Find the equation of the straight line shown.
• 9. y varies directly as the square root of x and
  y 5 when x 16.
• Find an equation connecting x and y. Find y
  when x 9.
• 10. Evaluate (5x2)3
• 11. Solve the equation 7x 4x2 0.
• 12. Multiply out the brackets and simplify
  (3? 2 1)(2? 2 1)

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Non Calculator - Test 13
1. The rectangle shown has an area of 84 sq.cm
Make an equation and find x. 2. Factorize
fully 25t3 t 3. Find 25 of 350 4.
Simplify the expression x(x-3) (x2)(x1) 5.
Evaluate 13.8 15.6 4.7 6. If f(x) 3x2
2x 1 , find the value of f(-2). 7. Write
?500 as a surd in its simplest form.
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• Find the gradient of the straight line shown.
• 9. y varies directly as the square of x and y
  40 when x 2.
• Find an equation connecting x and y. Find y
  when x 3.
• 10. Evaluate (yx3)4
• 11. Solve the equation x2 6x - 16 0.
• 12. Multiply out the brackets and simplify (?
  2 1)(? 2 1)

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Non Calculator Test 14
1. If sinx , find the exact value
of cosx. 2. Write the fraction
with a rational denominator in its simplest
possible form. 3. Find 9 of 36 4. If f(x)
3x 5 and f(t) 22 , find t. 5. A rectangle
has a length 5?6 and a breadth 5-?6 . Find
an expression for the perimeter in its simplest
form. 6. Factorise 9x2 12x 4 7. The
perimeter of a square is 14cm. Find the area. 8.
If x y 24 and y 2x , find the value of
y 9. Simplify 10. Solve the equation x2
3x
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Non Calculator Test 15
1. Simplify 2. Simplify 3. Solve the
equation 5x (2x 3) 1 4. If W
, change the subject of the formula
to M. 5. If x 9 and y 16 find the value of
6. Find the V.A.T. on an article costing
400. 7. If f(x) 5x 1 and f(t) -6 , find
t.
37
8. Simplify ? 20 ? 45 9. If A is an acute
angle and sinA , find the exact value of
tanA. 10. Solve the equation 2x2 5x
0 11. The diagram shows the graph of the
function y x2 6x. Find the
coordinates of point P, the minimum value of the
function. 12. Find the equation of the straight
line shown.
P
38
x
39
Non Calculator Test 16

• 1. Find 3 of 78
• 2. Evaluate
• 3. If a 2 , b -1 and c 3 find the value of
  ab bc
• 4. Evaluate 12 ? 4 6 ? 2
• 5. Factorise fully 2x2 3x 1
• 6. Simplify the algebraic fraction
• Write 56 as a fraction in its simplest form.
• 8. Solve the equation 2x2 5x 0
• 9. If 10 of a number is 17 , find the number.
• Find the value of x if x y 12 and x y
  11

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Non Calculator Test 17

• Evaluate
• 2. Evaluate 1.6 3.2 2.1
• Write as a single
  fraction
• 4. Write ?80 as a surd in its simplest form
• Factorize fully 6x2 13x 6
• 6. Find the gradient of the line which
• passes through the points (0,4) and (4,0)
• 7. Solve 6x (3x2) lt 4
• Remove the brackets (x 1)(x2 x - 3)
• If sinA , and A is an acute angle ,
  find the exact value of tanA.
• 10. If y varies directly as the square of x
  and x is trebled ,
• find the effect on y ?

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Non Calculator Test 18

• 1. Write the number 32.6904 correct to
• a) 1 decimal place b) 5
  significant figures
• Write the fraction with a rational
  denominator in its simplest
• possible form.
• 3. Find 50 of 6.42
• If f(x) 1-2x and f(t) 5 , find t.
• 5. Factorize fully 4x3 4x
• Make x the subject of the formula y mx c.
• The area of a square is 400cm2. Find the
  perimeter.
• If x 4 and y 16, find the value of
• 9. Simplify (x1)2 x(x-2)

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Non Calculator Test 19

• Simplify
• 2. Find x as a surd in its simplest form.
• If f(x) x x2 , find the value of f(-2).
• 4. Find 9 of 44
• The gradient of the line joining the points (0,2)
  and (2,t) is 4.
• Find the value of t.
• Write 40 as a fraction in its simplest form.
• If x 4? 3 and y 3? 3 find the value of 2xy
• 8. Solve the inequation 4x 2(1-2x) gt 5
• 9. If y varies directly as the square of x and x
  is doubled, find the effect on y
• 10. Solve the equations 3x 2y 16 , y
  x 2
• Factorize fully x4 81

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Non Calculator Test 20

• 1. Find the equation of the straight line with a
  gradient
• 3 which passes through the origin.
• If x -2, find the value of 3x2.
• Solve the equation x2 x 0.
• 4. y varies inversely as the square of x and y
  2 when x 2.
• Find a formula connecting x and y. Find y
  when x 4.
• Evaluate
• 6. Simplify ? 125 ? 75
• 7. The perimeter of the rectangle shown is 70cm.
  
• Make an equation and find x correct to 1 decimal
  place.

48

• Simplify
• Find 2 of 48.50
• Multiply out the brackets (x 2)3
• 11. Write in its simplest form
  with a rational denominator
• 12. Simplify the expression

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Non Calculator 21

• 1. Find 10 of 19
• 2. If x -1 and y -2 find the value of
  
• Solve the equation x2 3x.
• 4. Subtract 4.8 from 7.3
• 5. Remove the brackets (x 2) (x2 x 1)
• Write 8 as a fraction in its simplest form.
• Simplify
• 8. Find the gradient of the line 2x4y1 0
• 9. If y varies inversely as the square of x and
  y2 when x 3
• find a formula connecting x and y. Find y when x
  6.
• 10. If C , change the
  subject of the formula to F.

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Non Calculator Test 22

• If sinx and x is an acute angle, find the
  exact value of cosx.
• Write the fraction with a rational
  denominator in its simplest
• possible form.
• Find 2 of 80
• Evaluate of
• 5. A rectangle has a length 3?2 and a breadth
  5?2
• Find an expression for the area in its
  simplest form.
• 6. Factorise x2 x 6
• The perimeter of a square is 10cm. Find the area.
• If x 9 and y 4 , find the value of 4
• If f(x) 2x 5 and f(t) 23, find the value
  of t.

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Non Calculator Test 23

• Evaluate
• 2. Evaluate 11.6 13.2 2.5
• Remove the brackets (x 2)(2x2 x -1)
• Calculate the gradient of the line which passes
• through the points (5,2) and (-3,2).
• If f(x) 3 x x2, find the value of f(-3).
• Simplify
• 7 . Solve the equation x2 7x
• 8 . Simplify v45 v20 - v125
• 9 . If P 4(L B), change the subject of the
  formula to B.
• 10 . If y varies inversely as the square of x
  and x is doubled,
• find the effect on y?

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Non Calculator Test 24
1. Write down the equation of the trig.
function shown in the diagram. 2. If A is an
acute angle and sinA , find the exact
value of tanA, giving your answer as a surd
with a rational denominator. 3. Simplify the
expression 2x(x1) (2x1)(x-1) 4. Find the
exact value of cosA. 5. Solve the equation
6. If x 25 and y 4, find the exact value
of x -½ y ½
57

• Solve 2x 3y 21 , y 3x 4
• Find the equation of the line shown in the
  diagram.
• Simplify the expression shown
• 4
  
• 10. Find 15 of 20
• 11. Evaluate
• 12. Write v120 as a surd in its simplest form.

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Non Calculator Test 25
1. Find 5 of 60000 2. Evaluate ¼ of ( 10½ -
4) 3. A square has an area of 400 cm2. Find
the perimeter of the square. 4. Evaluate 1.52
2.52 5. Factorize fully x3 x 6. Solve 4
2(x 1) 9 7. If f(x) x2 1 find the value
of f(-2) f(2). 8. Write as a surd with a
rational denominator
9. A discount of 40 is offered on a
television set in a sale. Find the sale
price of the set. 10. State the gradient of
the line with equation x 4y 1
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Non Calculator Test 26

• Simplify
• Find the value of this expression when x 4.
• Find x as a surd in its simplest form
• 3. If f(x) 10 x x3 , find the value of
  f(-1).
• 4. y varies directly as x and y 6 when x 4.
  Find y when x 10.
• 5. Solve the equation x3 4x 0
• 6. Find the coordinates of point

62

• If x 4? 2 and y 5? 2 find the value of x3y
• 8. The graph shows the relation ? y varies
  inversely as the square of x
• Find the equation connecting x and y
• 9. If x 4, find the value of v(x2 48)
• 10. Find the point where the line 2x 3y -12
  0 cuts the x axis
• 11. Factorize fully x2 x 12
• 12. Remove the brackets (x 3)( x2 2x 3)

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Non Calculator Test 27
1. Simplify 2. Simplify 3. Solve the
equation 15 (2x 3) 1 4. If M
, change the subject of the
formula to T 5. Write as a single fraction
6. If 2x y 11 and x y 4 , find the
value of y. 7. If f(x) x2 4 and f(t) 32,
find t.
65
8. Simplify ? 242 - ? 98 9. If A is an acute
angle and cosA , find the exact value of
tanA. 10. Solve the equation x2 11x
0 11. The diagram shows the graph of the
function y x2 6x. Find the coordinates of
point P 12. Find the gradient of the straight
line shown.
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Non Calculator Test 28
1. Find 5 of 1800 2. If x -2 and y -4
, find the value of 3. A straight
line has equation 4x 3y 24. Find the
point where the line cuts the y axis. 4.
Subtract 4.76 from 12.38 5. Simplify the
algebraic fraction 6. Change to a
decimal.
68

• 7. A pupil scored in a Mathematics
  exam.
• What was his percentage mark?
• If f(x) ax2 5 and f(2) 33, find the value
  of a.
• 9. If y varies inversely as the cube of x and y
  1 when x 2.
• Find a formula connecting x and y. Find y when x
  1.
• 10. If e mc2 , change the subject of the
  formula to c.

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Non Calculator Test 29
1. Find the equation of the straight line shown
in the diagram. 2. If x -1, find the
value of x3 x2 3. Solve the equation 4x2
81 0. 4. P varies directly as the square of
Q and P 1 when Q 2. Find a formula
connecting P and Q. Find P when Q
10. 5. Evaluate 6. Simplify ? 200 - ?
128
71
7. The perimeter of the rectangle shown is
56cm. Make an equation and find x. 8.
Evaluate , when x 2 9.
Evaluate 100 25 5 10. Multiply out
the brackets (1-3x)(4x1) 11. Write with a
rational denominator 12. Simplify the
expression
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Non Calculator Test 30
1. What is the equation of the function shown
in the diagram? 2. If f(x) 4 ax3 and
f(-1) 5 , find a formula for f(x) and hence
find the value of f(3) 3. If x 10 , y -2
and t 3, find the value of 4. Simplify
3x4 (2x2)3 5. Simplify 6.
Evaluate 7. If x y 20 and y 4x , find
the value of y.
74

• Find the equation of the straight line shown.
• 9. Write x as a surd in its
• simplest form.
• 10. Evaluate 23.2 34.7 16.8
• 11. If , change the
  subject to M and hence find M when L10.
• 12. Solve the inequation -2x 9 5

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Non Calculator Test 31
1. The rectangle shown has an area of 72 sq.cm
Make an equation and find. 2. Factorize
fully 121x4 x2 3. Find 8 of 300. 4.
Simplify the expression 2x(x-3) (x2)(2x3) 5.
Evaluate 1.42 6. A Doctor has been given a
pay rise of 25. He now earns 60000 per
annum. How much did he earn before the pay
rise.
77

• 7. Write ?800 as a surd in its simplest form.
• Find the gradient of the straight line shown.
• 9. If x v5 2 and y v5 2, find the value
  of x2 y2.
• 10. Evaluate v(122 52)
• 11. Solve the equation 121 x2 0
• Multiply out the brackets and simplify
• (3? 7 1)(? 7
  1)

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Non Calculator Test 32

• 1. A straight line passes through the points
  (2,0) and (0,-2).
• Find its equation.
• Solve the equation Give your answer
  correct to
• 1 decimal place
• 3. Factorize fully 4x2 15x 9
• 4. y varies inversely as the square of x and x
  is doubled.
• Find the effect on y.
• 5. Evaluate
• 6. Simplify ? 32 - ? 18

80
7. The perimeter of the rectangle shown is
50cm. Make an equation and find x correct to 1
decimal place. 8. Simplify 9 Find 3
of 1000 10. If x -5, y 4 and t -2 , find
the value of x2yt. 11. Write
in its simplest form with a rational denominator.
12. Simplify the expression (x1)2 x(x1)
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Non Calculator Test 33

• Evaluate
• 2. Simplify the expression -4x(x-1) 4x(1-x) 3
  
• 3. Write as a single fraction
• 4. Write ?72 as a surd in its simplest form.
• 5. Factorize fully x2 16x 64
• 6. The point (t,5) lies on the line x y - 9
  0. Find the value of t.
• 7. Solve the inequation 5x (3x-2) lt - 4
• 8. Remove the brackets (2x 1)(x2 - x - 10)
• 9. A car costs 24000. In a sale it is
  reduced by 20.
• Find the sale price of the car.
• 10 A car travels a distance of 250 km in 2½
  hours.
• Calculate the average speed of the car in
  km per hour.

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Non Calculator Test 34

• 1. Simplify
• 2. Find x as a surd in its simplest form.
• 3. If P 2(LB), change the subject to L.
• 4. Find of 75
• 5. State the gradient of the line with gradient
  y 4.
• 6. Write 60 as a fraction in its simplest form.
• 7. If x 4? 3 and y 3? 3 find the value of
  xy2
• 8. Solve the equation x(x1) x2 10x 18
• 9. The point (4,2) lies on the curve with
  equation
• Find the equation of the curve.
• 10. Evaluate 8.4 11.2 (-7.8)
• Factorize fully x4 9x2

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86
Non Calculator Test 35
1. The rectangle shown has a perimeter of 70
cm. Make an equation and find x. 2.
Factorize fully 8x2 2x 15 3. Find 75 of
360 4. Simplify the expression 5. Write
as a single fraction 6. If f(x) x2 5x 6 ,
find the value of f(-3). 7. Write
as a surd in its simplest form with a rational
denominator.
87

• Find the gradient of the straight line shown.
• 9. y varies directly as the cube of x and y
  64 when x 4.
• Find an equation connecting x and y. Find y
  when x 6.
• 10. Simplify (2y3x4)3
• 11. Solve the equation x2 6x
• Multiply out the brackets and simplify
• (3? 2 1)(2? 2 1)

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Non Calculator Test 36
1. Write down the equation of the trig.
function shown in the diagram. 2. If A is an
acute angle and tanA , find the
exact value of cosA , giving your answer as a
surd with a rational denominator. 3.
Simplify the fraction 4. Find the exact
value of cosA in the diagram shown. 5. If f(x)
x3 -7 and f(t) 57, find t. 6. If x 49
and y 9 , find the exact value of
90

• 7. Find x if x y 17 and x y 8.
• 8. Find the equation of the line shown in the
  diagram.
• Simplify the expression shown
  . Hence evaluate this expression when
  x 3.
• 10. Find 125 of 40
• 11. Evaluate
• 12. If f(x) and f(t) , find
  t.

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