Algebra I
(MCQ):
What is the simplified form of 5(2x−3y)−4y?
A) 10x−19y
B) 10x−11y
C) 10x−y
D) 10x−3y−4y
A) 10x−19y
First, expand the parentheses by multiplying 5 by each term inside: 5(2x)=10x and 5(−3y)=−15y. Then, combine the like terms: 10x−15y−4y=10x−19y.
(Fill in the Blanks):
A class survey found that 12 students like blue and 18 students like red. The total number of students in the class is _______.
30
To find the total, you simply add the number of students who chose each colour: 12+18=30.
True or False:
Simple interest is calculated on the principal and the interest that has accumulated.
False
Simple interest is calculated only on the original principal. Compound interest is calculated on the principal and the accumulated interest.
True or False:
The empty set is a subset of every set.
True
By definition, the empty set is considered a subset of every set because it contains no elements that are not in the other set.
Given the equation x2+5x−6=0, what are the values of x?
x=1 and x=−6
Factorise the quadratic expression: (x−1)(x+6)=0. For the product to be zero, one of the factors must be zero.
x−1= 0 implies x=1
x+6= 0 implies x=−6
(MCQ):
Factorize the expression 4xy+8y2.
A) 4y(x+2y)
B) 4x(y+2y)
C) y(4x+8y)
D) 4(xy + 2y²)
A) 4y(x+2y)
The highest common factor of 4xy and 8y2 is 4y. Divide each term by 4y to get the terms inside the parentheses: 4y4xy=x and 4y8y2=2y.
(True or False):
The mode is always the number that is in the middle of a dataset.
False
The mode is the most frequent number. The median is the middle number.
(MCQ):
An item costs $200. After a 15% discount, what is the final price?
A) $170
B) $185
C) $175
D) $190
A) $170
The discount amount is 15% of 200, which is 0.15×200=30. Subtract the discount from the original price: 200−30=170.
(Fill in the Blanks):
In a universal set U=1,2,3,4,5 and a set A=1,3,5, the complement of A (A′) is ______.
2,4
The complement of a set contains all the elements in the universal set that are not in the original set. The complement of a set contains all the elements in the universal set that are not in the original set.
Solve the simultaneous equations:
x+y=7
x−y=3
x=5, y=2
Add the two equations together to eliminate y: (x+y)+(x−y)=7+3, which simplifies to 2x=10, so x=5. Substitute x=5 into the first equation: 5+y=7, so y=2.
(MCQ):
Which of the following is an example of a linear inequality?
A) x²+2x > 5
B) 3y=9
C) 5x−1≤2x+8
D) x+y=10
C) 5x−1≤2x+8
A linear inequality involves a linear expression with an inequality sign (<,>,≤,≥). Options A is a quadratic inequality, B is a linear equation, and D is a linear equation.
(MCQ):
What is the mean of the numbers 5, 8, 10, 12, 15?
A) 10
B) 15
C) 50
D) 12
A) 10
The mean is the sum of the numbers divided by the count of the numbers. Sum: 5+8+10+12+15=50. Count: 5. Mean: 50÷5=10.
(MCQ):
A television is bought on hire purchase. The deposit is $500, and there are 10 monthly payments of $250. What is the total hire purchase cost?
A) $2,500
B) $3,000
C) $3,500
D) $4,000
B) $3,000
Total payments are 10×250=2,500. The total hire purchase cost is the deposit plus the payments: 500+2,500=3,000.
(MCQ):
Which of the following is an example of a finite set?
A) The set of all natural numbers.
B) The set of all integers.
C) The set of all even numbers.
D) The set of letters in the word 'mathematics'.
D) The set of letters in the word 'mathematics'.
A finite set is a set with a countable number of elements. The letters in 'mathematics' can be counted as m,a,t,h,e,i,c,s. The other options are infinite sets.
Expand and simplify the expression 4(2x−3)+5x.
13x−12
First, distribute the 4 to the terms inside the parentheses: 4(2x)−4(3)=8x−12. Then, combine the like terms: 8x+5x−12=13x−12.
(Fill in the Blanks):
The simplified form of (y⁴)² is _______.
y8
When raising a power to another power, you multiply the indices. 4×2=8.
(MCQ):
A fair coin is tossed and a fair six-sided die is rolled. What is the probability of getting a 'head' and a number greater than 4?
A) 1/6
B) 1/4
C) 1/3
D) 1/2
A) 1/6
The probability of getting a head is 1/2. The probability of getting a number greater than 4 (5 or 6) is 2/6 or 1/3. To find the probability of both events happening, you multiply their probabilities: 1/2×1/3=1/6.
(Fill in the Blanks):
A loan of $10,000 is taken at a simple interest rate of 5% for 3 years. The total interest is _______ dollars.
A. 500
B.1500
C.15000
D. 5000
B.1500
Simple interest (I) is calculated as I=P×R×T.
P = 10,000
R = 5%=0.05
T = 3 years
I=10,000×0.05×3=1,500.
(MCQ):
In a class of 25 students, 18 play football and 12 play cricket. If every student plays at least one sport, how many students play both football and cricket?
A) 30
B) 25
C) 5
D) 5
D) 5
add the numbers of students playing each sport (18+12=30) and subtract the total number of students to find the overlap: 30−25=5.
Factorise the quadratic expression x²+6x+8.
(x+2)(x+4)
Look for two numbers that multiply to give 8 and add to give 6. The numbers are 2 and 4.
(True or False):
log₁₀1000=3.
True
The statement log101000=3 is asking: "To what power must 10 be raised to get 1000?". Since 103=10times10times10=1000, the statement is true.
(Fill in the Blanks):
In a bag of 10 marbles, there are 4 red and 6 blue. The probability of choosing a red marble is _______ (as a fraction).
2/5
The probability is the number of favorable outcomes divided by the total number of outcomes. The probability of choosing a red marble is 4/10, which simplifies to 2/5.
(MCQ):
An item with a cost price of $200 is sold for a profit of 20%. What is the selling price?
A) $220
B) $160
C) $240
D) $200
C) $240
First, find the profit amount: 20% of 200=0.20×200=40. Add the profit to the cost price: 200+40=240.
(MCQ):
In a class of 30 students, 20 play football and 15 play basketball. If 8 students play both sports, how many students play neither sport?
A) 3
B) 5
C) 7
D) 27
A) 3
First, find the number of students who play at least one sport. Use the formula: ∣FcupB∣=∣F∣+∣B∣−∣FcapB∣.
∣FcupB∣=20+15−8=27.
Solve the linear equation 2x+7=15.
x=4
Subtract 7 from both sides: 2x=15−7=8. Then, divide both sides by 2: x=8÷2=4.