Based Assessment (SBA) for CSEC Mathematics
The videos below are of me reading sections of the CSEC Mathematics syllabus that address the SBA.
Have you started your SBA as yet? Have you chosen your topic as yet? What topic are you researching?
Tuesday, February 14, 2023
Thursday, February 9, 2023
CSEC Mathematics Past Paper May 2022 Question 2 Solutions
Watch the video below for the solutions to the entire CSEC Mathematics May 2022 Past Paper.
Look at each of the images below. I recorded the video above and placed some images of screenshots of parts of those videos as images below. These images and notes below may enhance the learning process for some students.
Figure 1
Tell me, in the comments below, what you think I did in figure 1 above. I will type in my own comments here after some time.
Sunday, January 29, 2023
CSEC Mathematics Past Paper May 2022 Question 1 Solutions
CSEC Mathematics May 2022 past paper Question 1. Topic: Fractions
Question 1 a.
Download the past paper at
https://drive.google.com/file/d/1brXJs0qNrbMXA77jZS-S2Ek8sjF6hVET/view?usp=sharing
Watch the video below for the solutions to the entire paper. I recorded this video and placed some images of screenshots of parts of those videos below. These images and notes below may enhance the learning process for some students.
Take a look at this question. Part a. Topic: Fractions
Figure 1
Figure 2
Work it out and see what you get.
Figure 3
The 3 over 3 is equal to 1. The denominators multiply together and the denominators also multiply together. You get 3 divided by 4 for that part of the question.
Figure 4
The calculation now employs the common denominator method. You could also use the LCM method but remember that the LCM method is derived from the common denominator method.
Figure 5
The LCM method of adding 7/8 to 6/8 is now shown in the diagram below. Remember, this is the same as 7 * (1/8) + 6 * (1/8). 7 + 6 = 13 so there are 13 of the (1/8).
Figure 6
The next image shows that the fractions could be worked out by drawing circles to represent the whole item, then cutting it up into equal parts. Each equal part is represented by sectors of equal angles in the circle. Each circle is cut into eights. Each shaded sector is to be counted and placed as the numerator of the fraction, while the denominator is 8, the number of equal parts. Note that three quarters is the same as six eights.
Figure 7
We now obtain the answer, which is thirteen eights.
Figure 8
We now look at part a b i of the question. It asks you to simplify 8 divided by the cube of 0.4. You may use a calculator to do it but I will work it out in a different way.
Figure 9
Note that 0.4 is equal to 4 divided by 10. When you cube this, you get (4/10) times (4/10) times (4/10).
Figure 10
Figure 11
Figure 12
4/10 is equal to 2/5 when you divide both numerator and denominator by 2. I use 2/5 in the calculation. The image below shows this, and you get 8 divided by (8/125). When you have a number divided by a denominator and the denominator is a fraction, you must multiply the number by the reciprocal of the fraction. This gives you 8 times (125)/8. The result is 125.
Figure 13
Now, look at the next part of the question.
Figure 14
You cannot subtract the numbers 26.8 and 2.5 as yet. You have to work out the square root of 26.8 and 2.5 raised to the power of 3/2 first.
Figure 15
Look at the image above. The question says that children go to a Rodeo camp during the Easter holiday. Ms. Rekha buys bananas and oranges for the children at the camp. Bananas cost $3.85 per kg. Ms. Rekha buys 25 kg of bananas and receives a discount of 12%. You must find out how much money she spends on bananas.
To answer the question, you must multiply the cost per kg of bananas by the mass of bananas. This results in $96.25. With a 12 percent discount, you have to find 12 percent of the cost and then subtract that from the cost.
Figure 16
The amount left after the 12 % discount is $84.70.
Figure 17
You can also consider that if you get 12 percent off the price of $96.25, then that leaves
100 % - 12 % = 88 % percent. Find 88 percent of the cost. This leaves $84.70.
Figure 18
Now look at the next part of the question in the image above. It says that Ms. Rekha spends $165.31, inclusive of sales tax of 15% on oranges. Calculate the original price of the oranges.
A much easier case to calculate is when you are given the price before tax, then calculate the tax and add it. In the case presented here, you are given the total cost to include tax, and then you have to calculate what the price was before the tax was added.
A common mistake that students make is to find 15% of the price that has the tax, and the subtract. However, this is incorrect. The price before and after tax are different amounts of money, and 15% of two different amounts are different figures.
The way how I show this in the figure above is to use x to represent the price before tax, since this figure is not known. Whatever x is, we find 15% of it. The tax is 15/100 * x. The total amount is
x + 15/100 * x. This is equal to 165.31.
Figure 19
Follow the steps in the figure above. The calculations result in the answer $143.75
Figure 20
The next part of the questions says that the ration of the number of bananas to the number of oranges is 2:3. Furthermore, there are 24 more oranges than bananas. You are required to calculate the number of bananas that Ms. Rekha bought. Using Or to represent the number of oranges and B to represent the number of bananas, I divide them as Or/B and equate this to 2/3. Then, since the number of Oranges is 24 more than the number of bananas, then Or - B = 24. These make a pair of simultaneous equations, as shown in figure 20 above.
Figure 21
I multiply both sides by B as shown in figure 21 above. After that, I equate both values of Or.
Figure 22
Figure 22 shows that Or is equal to 2/3 B and 24 + B, therefore 2/3 B must be equal to 24 + B.
Figure 23
I simplified to get 3B = 72.
Figure 24
Dividing both sides by 3 yields B = 24 as shown in figure 24 above.
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