Download Task 3 - The Wise Man and the Chess Board

Stephenson College
Access Mathematics
Access Mathematics - Number and Algebra, unit RB1\2\EM\996
Test 2 - Calculator NOT allowed
Time allowed : 1 hour
Name : ____ANSWERS_____
1. Here is a list of numbers :
2, -41, 4, -5.5, 400, 0.125, 2, 9,  , -¼ , 11
NOTE : 9 = 3
Which of the listed numbers are :
a) natural or counting numbers
2, 4, 400, 11
(9 = 3)
b) integers
2, -41, 4, 400, 11
c) factors of 12
2, 4,
(9 = 3)
d) prime numbers
2, 11
(9 = 3)
e) irrational numbers
2, 
f) negative numbers
-41, -5.5
(9 = 3)
NB : list ALL the numbers which fit each category. Some categories may have
a long list, others a short list. Some of the numbers may go in more than one
category.
2. What is the meaning of the digit 2 in the following :
a) 3, 207,614
Two hundred thousand
b) 6.026
2
or two hundredths
100
3. Estimate the value of :
92
9.23²
81

4. Round
a) 71.239

15 – 7
14.8 - 6.917

8
to 3 s.f.
71.2
b) 23.0771
to 2 d.p.
23.08
c) 56,439
to 3 s.f.
56400
d) 0.001476 to 3 s.f.
0.00148
e) 0.010703 to 3 d.p.
0.011
Test 2, non-calculator
10
Page 1
Unit - Number & Algebra
Stephenson College
Access Mathematics
5. Simplify
a) 2a + 3b - x + 2y - 4a + b + x – y
-2a + 4b + y
2
b) 5x  2x
10 x
c) 6y³  4y
1.5 y2
6. Illustrate these results, which show the oscillation of a weight on a spring, on a
graph. Put time on the horizontal axis ( use 1 cm = 1 second) and displacement on
the vertical axis (use 1 cm = a displacement of 1 cm).
0
1
2
3
4
5
6
8
10
Time (seconds)
-10 0
7
0
-5
0
6
-3
2
Displacement (cm)
Displacement (cm)
8
6
4
2
0
-2 0
2
4
6
8
10
12
-4
-6
-8
-10
-12
time (seconds)
a) What is the displacement of the spring at time 6.5 secs.?
3.75 cm
b) At what times is the displacement -4 cm ? 0.6 secs, 3.8 secs, 4.2 secs
7. On holiday in Spain, Jane has a meal which costs 3000 pesetas. The exchange rate
is £1 = 220 pesetas. A service charge of 10% is added to the bill. What is the cost
in pesetas and in £ ?
3300 pesetas
= £15
8. Evaluate
a) 4³
= 4 × 4 × 4 = 64
b) 10 ²
= 100
c) 0.3²
= 0.3 × 0.3 = 0.09
d) 8 ÷ 0.2
= 80 ÷ 2 = 40
e) 0.4 × 500 = 20
f) 400
Test 2, non-calculator
= 20
Page 2
Unit - Number & Algebra
Stephenson College
9.
Access Mathematics
a)
Evaluate
11 squared ( i.e. 112 = 121
(LO 1.4)
b)
Evaluate
5 cubed
( i.e. 53 = 125
(LO 1.4)
c)
What is the reciprocal of
2
?
7
(LO 1.1)
d)
Evaluate
15 - 3 × 4 – (3 × 0.2)
15 – 12 – 0.6
g) e)
7
= 3.5
2
= 2.4
H = 3 a2 – 4ab
Calculate the value of
(LO 2.2)
where a = 4 and b = 2
H = 3 × 42 – 4 × 4 × 2
H = 48 – 32
10.
= 16
On the axes below choose a suitable scale and plot the points
A (3, 4)
B (0, -1.5)
C(-1, 4)
C
and
D(4.5, -3)
A
B
D
Test 2, non-calculator
Page 3
Unit - Number & Algebra