Multiple Choice Algebra
1. Find 4% of 5600.
Step: $4\% = \frac{4}{100} = 0.04$,
Calculate $0.04 \times 5600 = 224$.
Answer: a) 224
2. Calculate the difference $1 + (-7) - (-15)$.
Step: Simplify inside parentheses, $- (-15) = +15$.
Then $1 - 7 + 15 = 9$.
Answer: None of the options match 9, re-check calculation: $1 + (-7) - (-15) = 1 -7 +15 = 9$.
(Assuming a typo, closest answer to difference $8$ is b) 8)
3. Multiply fractions $\frac{3}{4} \times \frac{3}{2}$.
Step: Multiply numerators $3 \times 3 = 9$, denominators $4 \times 2 = 8$.
Result: $\frac{9}{8} = 1 \frac{1}{8}$.
Options given are fractions less than 1, none equal $\frac{9}{8}$.
Re-check fractions - if fractions provided are $\frac{3}{4} \times \frac{2}{3}$, then result is $\frac{3}{4} \times \frac{2}{3} = \frac{6}{12} = \frac{1}{2}$ which matches option c) $\frac{1}{2}$.
4. Convert 72 kilometers to miles.
Use $1$ km $= 0.621371$ miles.
Calculate $72 \times 0.621371 \approx 44.74$ miles.
Closest option: c) 45 miles.
5. Find average of 2.3, 4.0, 6.0.
Sum: $2.3 + 4.0 + 6.0 = 12.3$.
Average: $\frac{12.3}{3} = 4.1$.
None of options matches 4.1, check options again: options are a) 3.6 b) 3.9 c) 3.4 d) 3.8, so no correct option given, possible typo.
6. Jeton’s number problem:
Equation: $2x - 1 = 10$.
Solve: $2x = 11$, $x = \frac{11}{2} = 5.5$.
No option matches 5.5, no correct answer from options.
7. Expand $2y(5 - 3x)$.
Multiply: $2y \times 5 = 10y$, $2y \times (-3x) = -6xy$.
Answer: $10y - 6xy$.
Closest option: c) $10y - 6x$ (note $xy$ vs $x$ might be typo).
8. Find first four terms of $a_n = n^2 - 2n - 1$.
Calculate:
For $n=1$: $1 - 2 - 1 = -2$.
For $n=2$: $4 - 4 -1 = -1$.
For $n=3$: $9 - 6 - 1 = 2$.
For $n=4$: $16 - 8 -1 = 7$.
Sequence: -2, -1, 2, 7.
No options given match, likely typo.
9. Complete $5xy - [\_] = 15x^3 y^2$.
Given that $5xy - (3x^2 y^2) = 15x^3 y^2$?
Check options, correct exponent is $3x^2 y^2$ option c).
10. Identify line with negative direction.
A line $y = mx + c$ has negative direction if $m<0$.
Check options:
a) y = -2 (horizontal slope 0) no
b) y = 5 + 2x (slope +2) no
c) y = -2 - 3x (slope -3) yes
Answer: c)
11a. Perform fraction addition: $\frac{3}{4} + \frac{3}{2}$.
Common denominator 4, rewrite $\frac{3}{2} = \frac{6}{4}$.
Sum: $\frac{3}{4} + \frac{6}{4} = \frac{9}{4} = 2\frac{1}{4}$.
11b. Multiply fractions: $\frac{1}{4} \times \frac{2}{5} = \frac{2}{20} = \frac{1}{10}$.
11c. Subtract fractions: $\frac{3}{5} - \frac{1}{3}$.
Common denominator 15, rewrite: $\frac{3}{5} = \frac{9}{15}$, $\frac{1}{3} = \frac{5}{15}$.
Difference: $\frac{9}{15} - \frac{5}{15} = \frac{4}{15}$.
12. Divide 8100 denars in ratio 2:3:4.
Total parts: $2+3+4=9$.
Value per part: $\frac{8100}{9} = 900$.
First friend: $2 \times 900 = 1800$.
Second: $3 \times 900 = 2700$.
Third: $4 \times 900 = 3600$.
13. Solve $3(2x+5) - 2(x-5) = 61$.
Expand: $6x + 15 - 2x + 10 = 61$.
Simplify: $4x + 25 = 61$.
$4x = 36$, $x = 9$.
14. Fifth term = 43, seventh term = 57 of arithmetic sequence.
Set: $a_5 = a + 4d = 43$, $a_7 = a + 6d = 57$.
Subtract: $a_7 - a_5 = 2d = 14 \,\Rightarrow\, d = 7$.
Find $a$: $a + 4(7) = 43 \,\Rightarrow\, a + 28 = 43 \,\Rightarrow\, a=15$.
General term: $a_n = 15 + (n-1)7 = 7n + 8$.
15. Table for $y = 2x - 1$:
For $x=0$: $y=2(0)-1=-1$.
For $x=1$: $y=2(1)-1=1$.
For $x=2$: $y=2(2)-1=3$.