The 10th term of an AP is 32. If the first term is 3/2, what is the 4th term?
35/3
64
16
35/2
Correct answer is A
Tn = a + (n-1)d
10th term = 32
32 = 3/2 + 9d
9d = 32 - 3/2
9d = 61/2
d = 61/18
: T4 = 3/2 + 3(61/18)
T4 = 3/2 + 61/6 → 35/3
A rectangular pyramid has an area 24cm\(^2\) and height 7.5cm. Find its volume?
65.0cm\(^3\)
70.5cm\(^3\)
56.5cm\(^3\)
60.0cm\(^3\)
Correct answer is D
Volume of a rectangular pyramid = \(\frac{length * width * height}{3}\) or \(\frac{area * height}{3}\)
= \(\frac{24 * 7.5}{3}\) → \(\frac{180}{3}\)
Volume of the rectangular pyramid = 60cm\(^3\)
| F | R | C | G | S | M |
| 28% | 15% | 20% | 14% | 10% | 13% |
If the above information is represented on a pie chart. What angle represents his spending on food?
108.5
100.8
98.8
120.5
Correct answer is B
\(\frac{28 * 360}{100}\)
= 100.8º
Find the length of a chord 3cm from the centre of a circle of radius 5cm
8cm
5.6cm
7cm
6.5cm
Correct answer is A
Using pythagoras formula:
Hyp\(^2\) = adj\(^2\) + opp\(^2\)
5\(^2\) = opp\(^2\) + 3\(^2\)
5\(^2\) - 3\(^2\) = adj\(^2\)
4 = adj
length of the chord = 2 * 4 = 8cm
Simplify \(\frac{1}{3-√2}\) in the form of p + q√2
\(\frac{7}{3}\) - \(\frac{1}{7√2}\)
\(\frac{7}{3}\) + \(\frac{1}{7√2}\)
\(\frac{3}{7}\) - \(\frac{1}{7√2}\)
\(\frac{3}{7}\) + \(\frac{√2}{7}\)
Correct answer is D
Rationalization with conjugate \({3+√2}\)
\(\frac{1}{3-√2}\)
→ \(\frac{1 * [3+√2]}{[3-√2][3+√2]}\)
= \(\frac{3+√2}{9 -3√2 + 3√2 + √4}\)
= \(\frac{3+√2}{9 - 2}\) → \(\frac{3+√2}{7}\)
= \(\frac{3}{7}\) + \(\frac{√2}{7}\)