national 5 mathematics exam revision questionsexam revision questions exam: friday 4th may 2018 how...
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National 5 Mathematics Exam Revision Questions
Exam: Friday 4th May 2018
How to Revise
Use this booklet for homework Come to after school revision classes Come to the Easter holiday revision class There will be an immersion revision day before the exam Also revise AT HOME. A lot.
What to use to revise:
All the questions from this booklet Past Papers Course Notes
How to use these questions:
1. Try all the questions in this booklet once and check the answers. Ask for help asrequired:
If you are aiming for an A, you should focus mostly on questions marked A/B. If you are aiming for a C, you should mostly avoid the questions marked A/B.
2. Put a star next to all the questions you got wrong or required help (from teachers,friends or the notes) with.
3. Wait a few days and then try the starred questions a second time to see if you can managethem now.
4. If you cannot do them, ask for help again, wait a day or two and then try them again.
5. Repeat until you can do all the questions without needing help.
FORMULAE LIST
The roots of ( )2
2 40 are
2 x
b b acax bx c
a=
− ± −+ + =
Sine rule: sin sin sina b cA B C
= =
Cosine rule: cos cos2 2 2
2 2 2 2 or2
b c aa b c bc A Abc
+ −= + − =
Area of a triangle: sin12A ab C=
Volume of a sphere: 343V r= π
Volume of a cone: 213V r h= π
Volume of a pyramid: 13V Ah=
Standard deviation: s x xn
= −−
Σ( )2
1
or
( )22
1
xxns
n
ΣΣ −=
−, where n is the sample size.
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7. Find the equation of each of these straight lines:
(a) (b)
(c)
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(d)
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(i) (j)
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12.(a) (b)
(c) (d)
(e) (f)
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State the nature of the roots of the equation 3x² – 6x + 2 = 0
15. State the nature of the roots of the equation 2x² – x + 6 = 0
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Divide
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, using simultaneous equations.
(the first symbol is add, the second is divide)
Divide:
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11 ,210 3
2 10x 3,5x
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5 2))
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AB
AB
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107. 47
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111. Calculate the gradient and y-intercept of each line: (Hint: you will need to do some rearranging)
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133. Simplify the fractions:
(a) 2(3 1)
2(3 1)xx
(b) 2
2
4 8 42 2x xx
(c) 2
2
6 55 6
xx
xx
134. Simplify 75 3 48
135. Write as a single fraction in its simplest form:
(a) 2
48y x
y (b) 2
42ab
b (c) 3
3 84x y
x (d)
2
2
3a ab b
(e) 2
2 1a a
(f) 1 5
2y y (g)
3 21 3x x
(h)
3 65 4x x
136. State the nature of the roots of each equation:
(a) 2 6 9 0x x (b) 2 6 0x x (c) 23 3 1 0x x
137. Simplify 28 7 63
138. (a) Write down expressions for the areas of these two rectangles.
(b) The area of rectangle I is greater than the area of rectangle II. By how much is it greater?
139. Evaluate:
140. Simplify 54 2 6 150
141. a) The equation 2 4 2 0ax x has equal roots. Find the value of a.
b) The equation 23 2 0x x c has equal roots. Find the value of c.
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142.
143. a) The equation 22 8 0x bx has equal roots. Find the possible values of b.
b) The equation 2 2 0kx kx has equal roots. Find the possible values of k.
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Section B (Calculator Allowed)
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(b) After training the mean number of sit ups was 38 and the semi-interquartilerange was 10. Make two valid comments to compare the performances beforeand after training.
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(a) Sketch the graph of y = 3cos2x
(b) Sketch the graph of y = sin x + 1
(c) Sketch the parabola y = (x + 5)(x – 3), showing the intercepts with the x and y axes and the turning point.
It is estimated that house prices will increase at the rate of 3·15% per annum.A house is valued at £134 750. If its value increases at the predicted rate, calculate its value after 3 years. Give your answer correct to four significant figures.
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(a) Calculate the area of paper used to make the cone.
(b) Calculate the circumference of the base of the cone.
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(c) (d)
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117. (a) Sketch the graph of y = (x + 4)(x – 2), annotating the points where thegraph cuts the x and y axes and the turning point.
(b) Express x² – 8x + 20 in the form (x + a)² + b
(c) Hence sketch the graph of y = x² – 8x + 20, annotating the point where the graph cuts the y axis and the turning point.
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121. a) What is the frequency of the graph of y = 3sin4x ?b) What is the period of the graph of y = 5sin6x ?c) What is the period of the graph of y = 7cos(½x) ?
122. (a) Sketch the graph of y = (x + 9)(x – 5), annotating the points where thegraph cuts the x and y axes and the turning point.
(b) Express x² + 6x + 2 in the form (x + a)² + b
(c) Hence sketch the graph of y = x² + 6x + 2, annotating the point where the graph cuts the y axis and the turning point.
123.
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A B
C D
E
60 m
19.7 m
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124. Simplify the fraction:
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