1. A road sign says that no vehicles over 7.5 tonnes may use a bridge. My lorry weighs 4 tonnes, and I have 3.25 tonnes of presents and 4.75 of turkeys in the back of my lorry. How much am I over the bridge limit by?
a)3.5 tonnes
b)4.5 tonnes
c)2.5 tonnes
d) None - I should totally drive my heavy truck over the weak bridge
2. What is the probability of it raining on Monday and being cloudy on Tuesday if the probability of rain is 1/2 and the probability of clouds is 1/4?
a)3/4
b)1
c)1/8
d)1/4
3. What is 1.89240 to three significant figures?
a)1.89
b)1.892
c)1.8 x 103
d)1.9
4. I put 2,000 pounds in a bank and gain 0.50 percent interest for it every year. What is my new balance after one year?
a)10 pounds
b)2005 pounds
c)1990 pounds
d)2010 pounds
5. Use your answer for Q4 to find the new balance after the second year.
a)2020 pounds and five pence
b)Five pence
c)2010 pounds and five pence
d)1970 pounds and 95 pence
6. Look at the following equation, which determines the weight of an item.
P = w2 - 4
If w is the weight of the item and P is the price, find the price if the weight is three.
a)2
b)5
c)9
d)-1, so the item is free!
We'll be glad to check your answers.
1. To determine how much you are over the bridge limit, you first need to calculate the total weight of your lorry and its contents. Add the weight of your lorry (4 tonnes) to the weight of the presents (3.25 tonnes) and the weight of the turkeys (4.75 tonnes):
Total weight = 4 tonnes + 3.25 tonnes + 4.75 tonnes = 12 tonnes
Next, subtract the bridge limit (7.5 tonnes) from the total weight to find the excess weight:
Excess weight = Total weight - Bridge limit = 12 tonnes - 7.5 tonnes = 4.5 tonnes
Therefore, the answer is b) 4.5 tonnes.
2. To determine the probability of it raining on Monday and being cloudy on Tuesday, you need to multiply the probabilities of rain and clouds. The probability of rain is 1/2 and the probability of clouds is 1/4, so:
Probability of rain on Monday and clouds on Tuesday = (Probability of rain) x (Probability of clouds)
= (1/2) x (1/4)
= 1/8
Therefore, the answer is c) 1/8.
3. To round 1.89240 to three significant figures, you need to focus on the first three nonzero digits from the left. In this case, those digits are 1, 8, and 9. The fourth digit is 2, which is less than 5, so you round down. Therefore, the rounded value is 1.89.
Therefore, the answer is a) 1.89.
4. To calculate your new balance after one year with 0.50% interest, you need to multiply your initial balance by the interest rate and add it to your initial balance. The interest rate is 0.50%, which can be written as 0.005 in decimal form.
New balance = Initial balance + (Initial balance x Interest rate)
= 2,000 pounds + (2,000 pounds x 0.005)
= 2,000 pounds + 10 pounds
= 2,010 pounds
Therefore, the answer is d) 2010 pounds.
5. To find the new balance after the second year, you need to repeat the calculation from question 4 using the new balance from question 4 as the new initial balance.
New balance = Initial balance + (Initial balance x Interest rate)
= 2,010 pounds + (2,010 pounds x 0.005)
= 2,010 pounds + 10.05 pounds
= 2,020.05 pounds
Therefore, the answer is a) 2020 pounds and five pence.
6. To find the price when the weight is three in the equation P = w^2 - 4, substitute w = 3 into the equation:
P = (3)^2 - 4
P = 9 - 4
P = 5
Therefore, the answer is b) 5.