Equations and Inequalities
Solve for x
2x - 3 = x + 5
Factorize the following expression:
x2 + 5x + 6
(x + 2)(x + 3)
Simplify the following!
25:125
1:5
It takes a car 2 hours to drive 100 km. Calculate the average speed of the car!
50 km/h
If it costs $5 to make 2 cakes, how much money is needed to make 5 cakes?
$12.50
Provide both solutions for x in the following equation:
x2 - 7x + 6 = 0
x = 1
x = 6
Does this equation have a solution?
x2 +2x = x2 +2x - 3
Simplify the following!
3 hours : 200 minutes
9 : 10
How long does it take for an object moving at 14 km/h to travel 70 km?
5 hours
James wants to bake a cake. He follows a recipe which requires 1 cup of white sugar, half cup of butter, 2 eggs, 1 and a half cups of flour and half a cup of milk. However, James only has one egg, so he decides to adjust all the ingredients accordingly. How much milk should he use?
1/4 Cup
Write all possible integer values for x which satisfies the following inequality:
3x < x - 2 < 2x + 1
-3 < x < -1
A rectangle has sides with length of x meters and (x - 20) meters. If its area is 96m2, find the value of x!
In a bag, there are some marbles. The ratio of the amount of each different colored marble is
RED : GREEN : BLUE = 3 : 5 : 2
If there are 27 red marbles, how many marbles are in the bag?
90 marbles
Two people run in a 100m race. Person A first runs at a speed of 18 km/h for 10 seconds, then speeds up to 21 km/h for the remaining distance. Person B runs at a constant speed of 19 km/h throughout the race. Who would win?
Person A
The ratio of the angles in a triangle is 1 : 3 : 8.
What's the size of the largest angle?
120 degrees
Determine which of the following equations has ONE solution:
A. x2 - 3x + 2 = 0
B. x2 - 5x + 6 = 0
C. x2 + 2x + 1 = 0
C
How many solutions does the following expression have? (Hint: Use the quadratic formula)
x2 + 5x + 7 = 0
Team A has a 1 : 3 win-loss ratio, while team B has a 2 : 5 win-loss ratio. If team A and team B held a match against each other, who would be more likely to win?
Team B
Jason rides a bike and travels 10 km/h to the park from his house. Jake also rides a bike to the park, but at the speed of 12 km/h. If Jason's house is 2 km away from the park, and Jake's house is 3 km away from the same park, who will arrive there first?
Jason
A factory requires 5 machines to make a toy every 40 minutes. How many machines are required to make a toy in 8 minutes?
25 machines
Find the interval of x which satisfies the following inequality:
x2 + 2x + 5 < 3 - x
-2 < x < -1
Find the turning point (minimum value) of the following quadratic equation (Hint: Convert to completed square form)
y = x2 + 4x + 9
(-2,5)
Dave and Alexander had candies in the ratio 5 : 1. Dave gives him 14 candies and the ratio is now 3 : 2. How many candies did Alexander have initially?
10 candies
Alice drives to the store at different speeds. She drives at a speed of 20 km/h for 15 minutes, then slows down to 12 km/h for 5 minutes, and speeds up again to 40 km/h for the remaining distance. If the store is 10 km away, how long did she take to reach the shop? (in minutes)
26 minutes
Two right-angled triangles X and Y both have the same angles. Given that:
The ratio of the hypotenuse to the total length of all sides is 5 : 12
The ratio of X : Y = 3 : 4
The length of the smallest side in triangle X is 3 cm
Find the length of the hypotenuse of triangle Y (3 s.f.)
6.67 cm