MENTARI INTERCULTURAL SCHOOL JAKARTA
EXTENDED MATHEMATICS YEAR 4
DIAGNOSTIC TEST
SCHOOL YEAR 2020 -2021
Name: ________________
Grade/Sec: _____ CN: ___ Date: ______
Answer each of the following questions on a separate sheet of paper.
1. What is NOT true about the graph of y + 3 = -3 (x + 4)?
a. It has a gradient of -3.
b. It passes through the point (2, -21)
c. It intersects the y-axis at (0, -15)
d. It intersects the x-axis at (3, 0)
2.. Which quadratic equation corresponds to the following situation?
2x – 1
6x + 1
5x + 4
a. 7x2 – 24x + 16 = 0
b. 7x2 + 24x + 16 = 0
c. 7x2 – 24x – 16 = 0
d. -7x2 – 24x – 16 = 0
3. These two hexagons are similar. Determine the length in centimeters of the
diagonal BE.
A
B
3.4
F
A
C
1.3
E
B
D
?
F
C
2.0cm
E
D
4. If x varies directly as y and y = 2 when x = 5, find the value of x when y = 18.
5. The cost, c, in cents of lighting a 100-watt bulb varies directly as the time, t, in
hours, that the light is on. The cost of using the bulb for 1,000 hours is $0.15.
Determine the cost of using the bulb for 2,400 hours.
6. If y varies inversely as x and y = 5 when x = 2, find y when x = 12.
7. Bob’s dentist determined that the number of cavities developed in his patient’s
mouth each year is inversely proportional to the total number of minutes spent
brushing during each session. If Bob developed 4 cavities during the year and
spent only 30 seconds brushing his teeth each time, how many annual cavities will
Bob develop if he increases his brushing time to 2 minutes per session?
For numbers 8 – 10, find the product of each of the following expressions:
8. 3x(2x + 3)
9. (2x + 5) (3x – 4)
10. (x – 4)3
For numbers 11 – 16, factorize each of the following expressions COMPLETELY:
11. 3x2 + 27x
12. x2 - 5x + 6
13. 20x2 - 17x - 6
14. 9x2 + 30x + 25
15. 25x4  121y2
16. x3 4x + 2x2  8
For numbers 17 – 22, simplify each of the following expressions:
28 x 3
17.
35 x 5
20.
5 x 2  6x  7

x  1 3x  21
5 x  40
18.
4 x  32
2
21. m  2m  8 
8m  24
36 y 2
19.
12 y
2m  8
m 2  7m  12
22.
3
y

y  5 y 2  7 y  10
25.
2
7
4x  2

 2
x  6 x  2 x  4 x  12
For numbers 23 – 25, solve each of the following equations:
23.
3x
8
23


x7 x7 x7
24.
2
4
6
 
5( x  8) 5 ( x  8)
26. Make n the subject of the formula C =
an  1
n
27. Make t the subject in the formula v  u  at .
28. Make h the subject of the formula S = ar(r + h).
29. Given the formula b = -2a2 - T
(a) find the value of T when a = -4 and b = 3
(b) make a the subject of the formula.
30. Given the formula 2a2 = b2 + B
(a) find the value of B when a = 0.5 and b = 0.25
(b) make B the subject of the formula.
For numbers 31 – 35, solve each situation using any method.
31.
y  4x  1

2 x  y  37
32.
 5m  9n  21

2m  2n  14
33.
11x  2 y  27

21x  3 y  9
34. Two pan pizzas and two beef burritos provide 3100 calories. One pan pizza
and one beef burrito provide 1550 calories. How many calories are in each item?
35. A total of $10,000 is invested in two funds, Fund A and Fund B. Fund A pays
5% annual interest and Fund B pays 7% annual interest. The combined annual
interest is $630. How much of the $10,000 is invested in each fund?
Line A

Line B
y

Line C
y

























x
x
x





y








Line D
y
x





















Use graphs of Lines A-D to answer questions 36 - 40.
36. Which line(s) have a negative slope?
37. Which line has a slope of zero?
38. Which line has a y-intercept at (0, -2)?
39. Which line has a slope of ½?
40. Which line is the graph of the equation y = -x + 3?





