Practice :
1. Use <, > or = to complete each of these statements. (1/14/2/4/T)
a. 1/3 ___ 0.3
b. 12 ½% ______ 1/8
c. 7/12 _______ 5/9
2. y is proportional to x and y = 20 when x = 25. Find y when x = 10
3. y is inversely proportional to x and y = 20 when x = 25. Find y when x = 10
4a. Write 50 000 cm in kilometres.
A map is drawn to a scale of 1 : 50 000
b. The distance between two stations on the map is 12cm
Find the real distance between the stations in kilometres
c. The distance between two towns is 35 km. How far is this distance on the map?
5. Simplify 2x - 3(x - 2) [12/I/17/2/A]
3 5
6. The nth term of a sequence is given by 11 - 6n. Write down the first 3 terms of the sequence.
7. -2 ,1 , 4, 7
a. Write down the next 2 terms in this sequence
b. Find an expression for the nth term in this sequence. [17/I/24a/1,1/A]
<< END>>
1. Simplify 4x – 3(x – 3)
2. Factorise 2x2+ 5x – 3
3. Solve these simultaneous equations.
4x + 3y = 8
2x – y = 9
4. Anna invests $2000 for 3 years. She receives compound interest at 1.65% per year. How much is the investment worth at the end of the three years?
Short Practice 2
1.
2. Solve 2x= 5
3
3. y is proportional to x and y = 20 when x = 25. Find y when x = 10
4. y is inversely proportional to x and y = 20 when x = 25. Find y when x = 10
Short Practice 3
1. Simplify 4a2 x ab
b 6
2. Rearrange v2= u2+ 2as to make u the subject
3a. Sally has a map drawn to the scale 1 : 250 000.
The distance on the map between the airport and the city centre is 7.5cm
Calculate the actual distance, in kilometres between the airport and the city centre.
3b. The airport covers an area of 13km2
Calculate the area, in square centimetres, covered by the airport on the map.
Short Practice 4
1. Solve 4x + 5 = 3
2. Simplify 3x – 4(5 – 2x)
3. Solve these simultaneous equations
3x + 2y = 79
x + 4y = 68
4. Annie cycles at 20km/h for 2 hours 30 minutes from A to B. She then cycles a further 16 km in 1 hour 15 minutes from B to C. Calculate her average speed, in km/h, for the whole journey from A to C.
Short Practice 5
1. Solve 9 = 4
x + 2
2. Rearrange this equation to make h the subject
g = 3h – 2f
5
3. Felice is 10 years old and Lena is 6 years old.
a. Write the ratio Felice’s age : Lena’s age in the simplest form.
b. Felice and Lena are given some money to share in the ratio of their ages. Felice’s share is $30. Calculate Lena’s share.
c. A year later, they are given $54 to share in the ratio of their ages. Calculate Felice’s share.
Short Practice 6
1. Given that y = 6 – 3x, find the value of y when x = -4
2. Make d the subject of the formula c = 3d + 2e
3. The scale of a map is given as 1 : 50000
a. Rewrite the scale in the form of 1 cm to x km
b. A road on the amp is 18cm long. Find the actual length of the road in kilometres.
c. A lake has an area of 90km2. Find the area of the lake on the map in square centimetres.
Short Practice 7
1a. Make x the subject of a = bx + c (2,2/10/p1/19/T)
1b. Write as a single fraction in its simplest form 2 - 4
x 2x - 1
2a. Write 156 as a product of its prime factors. [1]
2b. Find the highest common factor of 156 and 390 [2]
Short Practice 8
1. A car travels for 1½ hours at 50km/h. It then travels for 2 hours at 65 km/h. Find the average speed for the whole journey.
2. Solve the simultaneous equation (3/12/p2/7b/A)
4x – 3y = 20
2x + 5y = -3
3. Solve (x – 5)(2x + 1) = 0
Short Practice 9
1. u = 2x + 1 v = x – 3 (2,2/15/p1/24/T)
Write an expression it its simple form, in term of x for
a. 3(v + 2) – 2v
b. u/2 + v/5
2a. Calculate 25 + 144 – 2 x 5 x 12 (1,2/5/p1/3/T)
2b. 6% of $450
3. Write the following in order of size, smallest first (2/14/p1/2/Y)
0.03 4% 1/30 Sin 2o
Short Practice 10
1. Round (1/13/1/3/T)
a. 25.6389 correct to 2 decimal places
b. 506423 correct to 3 significant figures
c. 0.00678472 correct to 4 significant figures
2. The scale of a map is given as 1 : 200 000 (112/5/p2/5/T)
a. Complete the following
Scale of map is 1cm to _____ km
b. Find the distance on the map between two towns that are actually 30 km apart.
c. On the map, a forest has an area of 5 cm2. Find the actual area of the forest in square kilometres.
Short Practice 11
1. Solve the simultaneous equations (3/14/2/7/T)
2x + 3y = 16
4x + 5y = 27
2. Use <, > or = to complete each of these statements. (1/14/2/4/T)
a. 1/3 ___ 0.3
b. 12 ½% ______ 1/8
c. 7/12 _______ 5/9
Short Practice 12
1. Simplify 6x ÷ 4 (2/13/1/3/T)
7 7
2. The ratio of the distance Mary runs to the distance she walks is 5:2. (2,2/14/2/6/T)
a. When she runs 4000m, how far does she walk
a. When she runs 4000m, how far does she walk
b. When she covers a total distance of 3500m during exercise, how far does she run?
3. Solve the equation (3/12/1/9/T)
3(2x + 50) = 12
Short Practice 13
1. Convert 100 kilometres per hour into metres per second. (2/13/1/2/T)
2. Solve the equation 4x + 2= 14 (5/13/1/5/T)
5
3a. Factorise a2+ 3a (12/13/1/6/T)
3b. Expand and simplify (x + 3)(x – 2)
Short Practice 14
1. Evaluate [1]
76.501
4.92 x 3.503
2a. Express 180 as the product of its prime factors
2b. Write down the smallest positive integers, k, such that 180k is a perfect square.
3. Factorise 3ax -6ay + bx – 2by
Short Practice 15
1. By rounding each number to 1 significant figure, estimate the value of
62.89 x 8.93
3.12
You must show your working.
2. A map is drawn to a scale of 1: 40 000. Find the actual length, in kilometer, of a road which is 6cm long on the map. (2/09/P1/7/A)
3. Factorise
(a) 4y2- 9
(b) x2– 6x - 9
Short Practice 16
1. Find the fraction exactly halfway between ¾ and 3/5. Give your answer in its simplest form. (2/11/p1/8/A)
2. Which of these ratio are equivalent to the ratio a : b?
a2: b2 3a:3b 1/b : 1/a a+1 : b+ 1
3. Solve the simultaneous equations
x + 4y = 1
3x + 2y = 13
Short Practice 17
1. Evaluate 78.6 ÷ 0.02 (1/12/p1/1a)
2.4 – 0.9
2. The distance between London and Tokyo is 9567 km. Write the distance to the nearest hundred. (1/12/p1/1b)
3. Solve
a. 4x + 5 = 3
b. x = 6
x + 5
Short Practice 18
1. Express 1/25 as a decimal. (1/13/p1/1b)
2. Express 30% as a fraction in its lowest terms.
3. Solve the inequality 4x ≥ 15 (1,2)
Solve 6 = 4
y - 3
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