Term 1 Year 10 Revision- Core

Understanding and Fluency

Indices

1. Simplify each of the following 2. Simplify each of the following and express
(a) × with positive indices :
(b) 2 × 3 a) 2

(c) ÷ b) 2 ×3

(d) c)
(e)
!× !
(f) 4 d)
!
(g) 2 ! "!
e) × #!
(h) 3 !

Exercise: 1.2 Questions 1,2, 3, 4 Exercise 1.5 Questions 1,2,3

Exercise 1.3 Questions 2,3, 4

Algebra and equations: Substitution

3. If $ = −6 and ( = −5 evaluate the 4. Calculate the unknown variable in the

following: following equation
(a) If * = + + - evaluate * if + = 16
a) $ − ( = 5 and - = 6
b) 3( − 5$

Exercise 2.2 Questions 1,2,3,4,5,6

Algebra and equations: Adding and subtracting algebraic fractions

5. Simplify each of the following: 6. Simplify each of the following by writing as

/ 0 single fractions:
a) − 0
a) +
10 0 02 0
b) +
/ 02 0 /
c) + b) −
0 10 02 0

Exercise 2.3 Questions 1,2,3, 4

Algebra and equations: Multiplying and dividing algebraic fractions

7. Simplify each of the following expressions 8. Simplify each of the following expressions
0 02 0 /
a) × a) ×
3 02/ 02 02
0
b) × b) ÷
02
/ 3
0 / 0 0 /
/
c) ÷
0 0
03 0
d) ÷
3

Exercise 2.4 Questions 1,2,3, 4

Algebra and equations: Solving simple and multi-step equations

9. Solve the following equations: 10. Solve the following equations:

a) ( − 75 = 46 a) 8 5 − 3 − 4 2 + 3 = 3
b) = 287 02/ 02
b) =
c) 6 + 8 = 44
0 0 /
d) 5 36 − 1 = 80 c) + =

Exercise: 2.5 Question 1-9. Exercise 2.6 Questions 1,2,3

Coordinate geometry: Sketching linear equations and determining linear equations

11. Q12. Find the equation of a straight line given

a) Plot the linear graphs defined by the the information in each case below.
following rules for the given range of values a) Gradient= -1 y intercept= -4
= −2 + 3
b) Gradient= -3 Point= (1,2)
-6 -4 -2 0 2 4 6 c) A line that passes through the points
(-1,4) and (3,2)
b) Sketch the graph of the following linear d)
equation using the and intercepts.
= −5 + 20

c) Sketch the graph of =2

Exercise: 3.2 Question 2,3,4,5,6 Exercise: 3.3 Question 1,2,3,4,5

Coordinate geometry: Parallel and Perpendicular lines

Q13. Q14.
a) Find the equation of the line that
a) Find whether AB is parallel to CD given
passes through the point (4,-1) and is
these sets of points:
parallel to the line with equation
A(4,13) B(2,9) C(0,-10) D(15,0)
=2 −5
b) Determine whether AB is perpendicular
b) Find the equation of the line that
to CD given the set of points
passes through the point (8,3) and is
A(1,6) B(3,8) C(4, -6) D(-3, 1)
perpendicular to a line with a gradient
of 4.

Exercise: 3.6 Question 1,2,6,7,8

Simultaneous equations: Graphical solution and substitution method

Q15. Q16.
a) Solve the following simultaneous
a) Use the graphs to find the solution of
equations using the substitution
the simultaneous equations
method.
i) 3 + 2 = 33
= 41 − 5

ii) 3 +4 =2
=7+5

iii) =3 +8
= 7 − 12

b) For the following simultaneous

equations, use substitution to check if
the given pair of coordinates is a
solution.
(7,5) 3 + 2 = 31
2 + 3 = 28
Exercise: 4.2 Questions 1,2 Exercise 4.3 Questions 1,2
Problem Solving and Reasoning

1. The surface area of a sphere is given by the formula 9 = 4:; where ; is the radius
of the sphere.
a) Find the surface area of a sphere that has a radius of 5cm.
b) What is the radius of a sphere that has a surface area equal to 500cm2?

2. The surface area of a cube with side length cm is given by 9 = 6 . Find the side
length (correct to one decimal) of a cube that has a surface area of 37.5cm2.

3. Last week Maya broke into her money box. She spent one-quarter of the money on
a birthday present for her brother and one-third of the money on an evening out
with her friends, leaving her with $75. How much money was in her money box?

4. Last week’s school fete was a great success, raising a good deal of money. Three-
eighths of the profit came from sales of food and drink, and the market stalls
recorded one-fifth of the total. A third of the profit came from the major raffle, and
the jumping castle raised $1100. How much money was raised at the fete?

5. A fun park charges a $12.50 entry fee and an additional $2.50 per ride.
a) Complete the following table of values relating the total cost to the number of rides.

b) Find a linear equation relating total cost to the number of rides.

c) Using algebra, calculate the cost for 7 rides.

6. The temperature of the air (ToC) is related to the height above sea level (< =>-;>?)
by the formula @ = 18 − 0.005<.
a) What is the temperature at the heights of:
i) 600 m
ii) 1000m
iii) 3000m

7. You are investigating prices for having business cards printed for your new games
store. A local printing company charges a flat rate of $250 for the materials used and
$40 per hour for labour.
a) If < is the number of hours of labour required to print the cards, construct an
equation for the cost of the cards A.
b) You have budged $1000 for the printing job. How many hours of labour can you
afford? Give your answer in hours and minutes.
Understanding and Fluency Answers

c)

Q1. Q8.
0 /
a) a)
02/ 02
b) 6
b)
c) 0 02

d) Q9.
e) 1 Q12.
a) 121
f) 4
b) 16.9 a) =− −4
g) 16
c) 6 b) = −3 + 5
h) 9 /
d) 5 c) = +
Q2. d) =2
Q10.
a) # Q13.
a)
b) 0"3 a) No
/
b) 3
c) b) Yes
c) /
d) Q14.
Q11.
e) ! a) =2 −9
a) /
b) =− +5
Q3.

a) -1
b) 15

Q4. 46 Q15.
Q5. a) =2 = −1
0 b) No
a)
b)
/ 0 Q16.

c) a) (7,6)
10
b) (2,-1)
Q6. b) c) (5,23)
0 2/ 0
a)
02 0
0
b) 02 0

Q7.
0
a)
3
0
b)
3
/
c)
3
d)
Problem solving answers

Q1.

a) 314.2cm2
b) 6.3cm

Q2. 2.5cm

Q3. $180

Q4. $12 000

Q5.

a)

Number of 0 2 4 6 8 10
rides
Cost ($) 12.50 17.50 22.50 27.50 32.50 37.50

b) A = 12.50 + 2.50; where C=Cost and r= number of rides

c) $30

Q6.

i) 15

ii) 13

iii) 3

Q7.

a) A = 250 + 40<
b) 18 hours and 45 minutes