Grade B Maths Assessment Test 1 Name: Class: Date: A(2) B(5) C(14 ...
Grade B Maths Assessment
Test 1
Name:
A(2)
A
Class:
B(5)
C(14)
D(11)
E(13)
Date:
Total Score (45)
Grade
Number and the number system
1. (a) Write
4 as an exact decimal 9 ..............................................1 mark (B/1)
(b) Write 0.5454545454.................. as a fraction
..............................................1 mark (B/1)
B
Calculating
2. (a) £5430 is put into a savings account offering a 4.7% interest per annum. What is the amount of money in the account after 5 years?
1 mark (B/2)
(b) A jumper was reduced by 43% to £31.92. What was the original cost of the jumper?
1 mark (B/2)
3. (a) (i) Express 432000 in standard form
................................ 1 mark (B/3)
(ii) Express 3.2 x 10-2 as an ordinary number
................................ 1 mark (B/3)
(b) Work out 8.4 x 10-3 x 6.2 x 10-5 Give your answer in standard form ................................ 1 mark (B/3)
C 4.
Algebra Factorise the following expressions: (a) x2 + 3x -10 1mark (B/4)
(b) x2 - 25
1mark (B/4)
5. Expand the following : (a) (4b + 1)(3b – 2)
...........................................................1 mark (B/5)
(b) (p + q)2
...........................................................1 mark (B/5)
(c) x2 + 3x – 4 = (x – 1)(x + 4) Use the above to solve the equation x2 + 3x – 4 = 0
x - ............ and x = ........... 2 marks (B/5) 6. Make b the subject of this formula: Show each stage of your working out
4a + 6b = 11.
b = ......................... 1 marks (B/6) 7.
Surface area of a cone: S = πr + πrl 2
Work out S when r =
4 85 cm and l = 7.5cm
Give your answer correct to 3 significant figures S = ......................... 1 mark (B/7)
8. Show by shading, the region where:
x ≥ 1, y ≥ 0 and x+ y ≤ 4
2 marks (B/8)
9. Match each graph to the correct equation. A
B
y
C
y
x
D
y
x
E
y
x
y
x
x
Graph ................ shows the equation y 2x – 6 Graph ................ shows the equation y 6x3 Graph ................ shows the equation y 6 – x Graph ................ shows the equation y x2 – 6 Graph ................ shows the equation y 1 6x
2 marks (B/9)
10. The diagram shows the graph of y = x2. On the same axes sketch the graph of y = x2 + 2
2 marks (B/10)
D
Shape, Space and Measure
11. The diagram shows five triangles. All lengths are in centimetres. 6
B
7
7
7
D
6 8 9 6
A 8
(a)
7
8
E
7
10.5
C 9 6
Write the letters of two triangles that are congruent to each other. ..................... and ..................... 1 mark (B/11)
Explain how you know they are congruent. ................................................................................................................................................................... 1 marks (B/11) (b)
Write the letters of two triangles that are mathematically similar to each other but not congruent .................... and .....................1 mark (B/11) Explain how you know they are mathematically similar. ..............................................................................................................................………………………1 mark (B/11)
(c) The triangles below are similar. b
b
m 10 c
p
cm
a 8 cm
a
m 12 c
What is the value of p? Show your working.
p ......................... 1 mark (B/11)
12. (a)
Calculate the length w
w
28 cm 52°
w ......................... cm (b)
2 marks (B/12)
Calculate the size of angle x
60 cm
42 cm
x
Not drawn accurately
x ...............................° 2 marks (B/12) 13.
The letters x, y and z represent lengths. Place a tick in the appropriate column for each expression to show whether the expression can be used to represent a length, an area, a volume or none of these. None of Expression Length Area Volume these x+y+z xyz xy + yz + xz 2 marks (B/13)
E
Data Handling
14 (a) The cumulative frequency graph shows some information about the ages of 100 people.
100
90
80
70
60 Cumulative Frequency 50
40
30
20
10
0
20
40
60 Age (years)
80
100
120
(a) Use the graph to find an estimate for the number of these people less than 70 years of age. .......................... 1 mark (B/14) (b)
Use the graph to find an estimate for the median age. .......................... years 1 mark (B/14)
(c)
Use the graph to find an estimate for the interquartile range of the ages.
.......................... years 2 marks (B/14) 15. The table shows the means and interquartile ranges of two batsmen’s scores in their last 20 innings. Mean
Interquartile range
Mike
43.4
6.4
Alex
47.8
15.2
Which batsman would you select? Explain why ................................................................................................................................................. 1 mark (B/15)
16 (a) The probability that Steve is late leaving work is 0.7. The probability that George is late leaving work is 0.45. What is the probability that Steve is late leaving work, and George is not late leaving work?
.................... 2marks (B/16) (b) A biased spinner is constructed so that the probability that it lands on 3 is ⅜ and the probability that it lands on 4 is ⅓ What is the probability that it lands on either a 3 or a 4?
.................... 2marks (B/16) 17.
Loren has two bags. The first bag contains 3 red counters and 2 blue counters. The second bag contains 2 red counters and 5 blue counters. Loren takes one counter at random from each bag. (a)
Complete the probability tree diagram. Counter from first bag
Counter from second bag Red 2 7
Red 3 5 ...... Blue Red ...... ...... Blue
...... Blue
2marks (B/17)
(b)
Work out the probability that Loren takes one counter of each colour. ............................................... 2marks (B/17)
Test 1
Name:
A(2)
A
Class:
B(5)
C(14)
D(11)
E(13)
Date:
Total Score (45)
Grade
Number and the number system
1. (a) Write
4 as an exact decimal 9 ..............................................1 mark (B/1)
(b) Write 0.5454545454.................. as a fraction
..............................................1 mark (B/1)
B
Calculating
2. (a) £5430 is put into a savings account offering a 4.7% interest per annum. What is the amount of money in the account after 5 years?
1 mark (B/2)
(b) A jumper was reduced by 43% to £31.92. What was the original cost of the jumper?
1 mark (B/2)
3. (a) (i) Express 432000 in standard form
................................ 1 mark (B/3)
(ii) Express 3.2 x 10-2 as an ordinary number
................................ 1 mark (B/3)
(b) Work out 8.4 x 10-3 x 6.2 x 10-5 Give your answer in standard form ................................ 1 mark (B/3)
C 4.
Algebra Factorise the following expressions: (a) x2 + 3x -10 1mark (B/4)
(b) x2 - 25
1mark (B/4)
5. Expand the following : (a) (4b + 1)(3b – 2)
...........................................................1 mark (B/5)
(b) (p + q)2
...........................................................1 mark (B/5)
(c) x2 + 3x – 4 = (x – 1)(x + 4) Use the above to solve the equation x2 + 3x – 4 = 0
x - ............ and x = ........... 2 marks (B/5) 6. Make b the subject of this formula: Show each stage of your working out
4a + 6b = 11.
b = ......................... 1 marks (B/6) 7.
Surface area of a cone: S = πr + πrl 2
Work out S when r =
4 85 cm and l = 7.5cm
Give your answer correct to 3 significant figures S = ......................... 1 mark (B/7)
8. Show by shading, the region where:
x ≥ 1, y ≥ 0 and x+ y ≤ 4
2 marks (B/8)
9. Match each graph to the correct equation. A
B
y
C
y
x
D
y
x
E
y
x
y
x
x
Graph ................ shows the equation y 2x – 6 Graph ................ shows the equation y 6x3 Graph ................ shows the equation y 6 – x Graph ................ shows the equation y x2 – 6 Graph ................ shows the equation y 1 6x
2 marks (B/9)
10. The diagram shows the graph of y = x2. On the same axes sketch the graph of y = x2 + 2
2 marks (B/10)
D
Shape, Space and Measure
11. The diagram shows five triangles. All lengths are in centimetres. 6
B
7
7
7
D
6 8 9 6
A 8
(a)
7
8
E
7
10.5
C 9 6
Write the letters of two triangles that are congruent to each other. ..................... and ..................... 1 mark (B/11)
Explain how you know they are congruent. ................................................................................................................................................................... 1 marks (B/11) (b)
Write the letters of two triangles that are mathematically similar to each other but not congruent .................... and .....................1 mark (B/11) Explain how you know they are mathematically similar. ..............................................................................................................................………………………1 mark (B/11)
(c) The triangles below are similar. b
b
m 10 c
p
cm
a 8 cm
a
m 12 c
What is the value of p? Show your working.
p ......................... 1 mark (B/11)
12. (a)
Calculate the length w
w
28 cm 52°
w ......................... cm (b)
2 marks (B/12)
Calculate the size of angle x
60 cm
42 cm
x
Not drawn accurately
x ...............................° 2 marks (B/12) 13.
The letters x, y and z represent lengths. Place a tick in the appropriate column for each expression to show whether the expression can be used to represent a length, an area, a volume or none of these. None of Expression Length Area Volume these x+y+z xyz xy + yz + xz 2 marks (B/13)
E
Data Handling
14 (a) The cumulative frequency graph shows some information about the ages of 100 people.
100
90
80
70
60 Cumulative Frequency 50
40
30
20
10
0
20
40
60 Age (years)
80
100
120
(a) Use the graph to find an estimate for the number of these people less than 70 years of age. .......................... 1 mark (B/14) (b)
Use the graph to find an estimate for the median age. .......................... years 1 mark (B/14)
(c)
Use the graph to find an estimate for the interquartile range of the ages.
.......................... years 2 marks (B/14) 15. The table shows the means and interquartile ranges of two batsmen’s scores in their last 20 innings. Mean
Interquartile range
Mike
43.4
6.4
Alex
47.8
15.2
Which batsman would you select? Explain why ................................................................................................................................................. 1 mark (B/15)
16 (a) The probability that Steve is late leaving work is 0.7. The probability that George is late leaving work is 0.45. What is the probability that Steve is late leaving work, and George is not late leaving work?
.................... 2marks (B/16) (b) A biased spinner is constructed so that the probability that it lands on 3 is ⅜ and the probability that it lands on 4 is ⅓ What is the probability that it lands on either a 3 or a 4?
.................... 2marks (B/16) 17.
Loren has two bags. The first bag contains 3 red counters and 2 blue counters. The second bag contains 2 red counters and 5 blue counters. Loren takes one counter at random from each bag. (a)
Complete the probability tree diagram. Counter from first bag
Counter from second bag Red 2 7
Red 3 5 ...... Blue Red ...... ...... Blue
...... Blue
2marks (B/17)
(b)
Work out the probability that Loren takes one counter of each colour. ............................................... 2marks (B/17)
