Transcript Kilsyth Academy National 5 Maths Revision Exercises Booklet

Kilsyth Academy
National 5 Maths
Revision Exercises
Booklet Number
National 5 Maths Mixed Revision Exercises
Ex 1
No Calculator for Q1
No Calculator for Q1
1. Work out the standard deviation for these
numbers -
2
3
4
4
5
7
9
10
2. Expand -
3(2x – 1)(x + 3)
3. Factorise - 2x2 + 7x – 4
4. Work out the gradient of the line joining
the points A(-2, 4) and B(5, -1).
5. Sketch the graph of y = 2sinx for 0º ≤ x
≤ 360º.
6. Solve the equation 4sinx + 1 = 0 for 0
< x ≤ 360.
7. Factorise 9a2 – 25
8.
M = R2t – 7
Change the subject of the formula to R.
9. Solve algebraically the inequality
2 + 5y ≥ 8y – 16
10. Solve algebraically the system of
equations
2p + 4q = -7
3p – 5q = 17
11. Work out the length of BC in the triangle
below.
12. Write down the exact value of sin30º.
13. Work out
1. Work out the standard deviation for these
numbers -
13, 20, 16, 24, 19, 16
2. Work out the equation of the line joining
the points P(-1, -1) and (0 , 3)
3. Change the subject of the formula to t
4. Sketch the graph of y = cos2xº for 0 ≤ x
≤ 360.
5. Solve algebraically the equation x2 – 6x =
0.
6. Solve the equation
for 0 ≤ x ≤ 360.
7cosxº - 2 = 0,
7. a) Factorise
Hence, simplify
2x2 – 5x – 3
b)
8. Solve the equation - 5x2 – 13x – 6 = 0
9. Solve, algebraically, the system of
equations 3x + 5y = 11
2x + 4y = 9
10. Solve the equation - x2 + 2x – 6 = 0
Give your answers correct to 2 significant
figures.
11. In the triangle below, work out the length
of PR.
1. Expand -
5(2x + 3)2
2. Write down the exact value of tan45º.
3. Simplify - a)
b)
4. Solve, algebraically, the equation 3t2 – 5t – 2 = 0
5. Find the perimeter of this shape.
(Give your answer to 3 significant figures).
6. Solve, algebraically, the equation 5sinxº - 2 = 0 ,
for 0 ≤ x < 360.
7. Find the gradient of the line passing
through the points (5 , -2) and (-3 , -1)
8. If
,
find
.
9. The data below shows the number of
letters in a sample of 40 words from the new
Henry Trotter book.
8 , 2 , 4 , 3 , 1 , 4 , 10 , 6 , 4 , 4 , 3 , 7 , 3 , 3 ,
4,6,2,6,2,3
5,4,7,2,4,2,3,3,1,7,7,6,1,3,6
, 3 , 5 , 1 , 4 , 11
a) Work out the quartiles Q1, Q2, and Q3.
b) Show this information in a boxplot.
c) Work out the semi-interquartile range.
1. Work out the standard deviation for these
numbers –
12 13 14 14 15 17 19 20
2. Solve, algebraically, the system of
equations x + 2y = 0∙6
4x + 3y = 1∙3
3.
The diagram shows the graph of y = ksinaxº,
0 ≤ x < 360.
Find the values of a and k.
4. Solve, algebraically, the equation x2 = 9x .
5. g(t) = 5t – 4t2
Find g(-2).
6. Solve < 360.
6sinx° + 2 = 0
for 0 ≤ x
7. The data below shows the takings (in
pounds) over a fortnight, for Sugar’s Sweet
Shop.
546, 283, 420, 692, 189, 364, 475, 263,
349, 731, 684, 319, 482, 353
Show this information in an ordered stemand-leaf diagram.
(Remember to include a key!)
8. Draw a sketch of the line with equation y
= 2x  3.
Your sketch must indicate clearly the
coordinates of 2 points on the line.
9. Express as a single fraction in its simplest
form
10. Solve, algebraically, the equation x2 = 10  3x
1.
The diagram shows the graph of y = acosbxº,
0 ≤ x < 360.
Find the values of a and b.
2. Solve, algebraically, the equation 4x2  9 = 0
3. Express
in its simplest form.
5. Work out the equation of the line which
passes through the points (2, 1)
and (0, 2).
6. Sketch the graph of the function x2  2x  8
for 4 ≤ x ≤ 6.
y=
What is the minimum value of this function?
7. h = k + 5√t
this formula to t.
Change the subject of
8. Simplify –
9. Solve, algebraically, the equation - 5
tanxº + 5 = 0
for 0 ≤ x ≤ 180.
10. Solve the following equation - x2  4x +
2=0
(Give your answer to 2 decimal places).
11. Given that f(p) = p2  4p, evaluate f(3).
1. Evaluate –
a) 8·13 – 6
b)
2. Solve the inequality 8 – 4x > 3(x + 2)
3. Given that
4. a) Factorise
b) Hence simplify
5.
Change the subject of the formula to p.
7. Simplify - a)
b)
8. An ant weighs approximately kilograms.
A sparrow is 26 times heavier.
Calculate the weight of the sparrow, give your
answer in scientific notation.
9. A laptop is sold for £850. This price
includes VAT at 17·5%.
Calculate the price of the laptop without
VAT.
10. Solve the equation
Give your
answers correct to 1 decimal place.
11.
The diagram shows part of the graph of y =
sinx°.
The line y = 0·6 is drawn and cuts the graph
of y = sinx° at A and B.
Find the x co-ordinates of A and B.