Formulas: Formulas
For ACT Students
The ACT is a timed exam...60 questions for 60 minutes
This implies that you have to solve each question in one minute.
Some questions will typically take less than a minute a solve.
Some questions will typically take more than a minute to solve.
The goal is to maximize your time. You use the time saved on those questions you
solved in less than a minute, to solve the questions that will take more than a minute.
So, you should try to solve each question correctly and timely.
So, it is not just solving a question correctly, but solving it correctly on time.
Please ensure you attempt all ACT questions.
There is no negative penalty for a wrong answer.
For JAMB and CMAT Students
Calculators are not allowed. So, the questions are solved in a way that does not require a calculator.
For WASSCE Students
Any question labeled WASCCE is a question for the WASCCE General Mathematics
Any question labeled WASSCE-FM is a question for the WASSCE Further Mathematics/Elective Mathematics
For GCSE Students
All work is shown to satisfy (and actually exceed) the minimum for awarding method marks.
Calculators are allowed for some questions. Calculators are not allowed for some questions.
For NSC Students
For the Questions:
Any space included in a number indicates a comma used to separate digits...separating multiples of three digits from
behind.
Any comma included in a number indicates a decimal point.
For the Solutions:
Decimals are used appropriately rather than commas
Commas are used to separate digits appropriately.
Solve all questions
Use at least two methods whenever applicable.
Show all work
The total profit for the 3 days was $2,525
The profit, in dollars, is shown for each of the 3 days in the bar graph below.
The Sunrise Preschool plans to extend the book fair for an additional day.
To estimate the profit for Day $4$, the preschool uses the geometric sequence that most closely approximates the daily profits for the 3 days the book fair has been held.
Among the following, which is closest to the preschool's estimated profit for Day $4$?
$ A.\:\: \$0 \\[3ex] B.\:\: \$75 \\[3ex] C.\:\: \$140 \\[3ex] D.\:\: \$200 \\[3ex] E.\:\: \$275 \\[3ex] $
$ \underline{Profit} \\[3ex] Day\:1...clearly\:\:visible = \$1500 \\[3ex] \rightarrow first\:\:term = a = 1500 \\[3ex] Day\:2...not\:\:clear...skip\:\:for\:\:now \\[3ex] Day\:3...a\:\:little\:\:over\:\:\$300...assume\:\:\$310 \\[3ex] \rightarrow third\:\:term = 310 \\[3ex] first\:\:term + second\:\:term + third\:\:term = 2525...total\:\:profit \\[3ex] 1500 + second\:\:term + 310 = 2525 \\[3ex] 1810 + second\:\:term = 2525 \\[3ex] second\:\:term = 2525 - 1810 \\[3ex] second\:\:term = 715 \\[3ex] GS:\:\: 1500, 715, 310, fourth\:\:term \\[3ex] fourth\:\:term = Day\:4 \\[3ex] r = \dfrac{715}{1500} \\[5ex] fourth\:\:term = 310 * \dfrac{715}{1500} \\[5ex] fourth\:\:term = \dfrac{221650}{1500} \\[5ex] fourth\:\:term = 147.7666667 \\[3ex] Closest\:\:to\:\:the\:\:preschool's\:\:estimated\:\:profit\:\:for\:\:Day\:4 \approx \$140\:(based\:\:on\:\:the\:\:options) $
The Santanas' rectangular house is 40 feet wide and 30 feet long, and their rectangular house is 75 feet wide and 100 feet long.
The Santanas have a rectangular garden in the back corner of their yard that is 30 feet wide and 25 feet long.
The garden currently contains 48 flower bulbs: 10 tulip bulbs, 18 daffodil bulbs, and 20 crocus bulbs.
Beginning next year, Mr. Santana will increase the number of bulbs in the garden each year so that the numbers form a geometric sequence.
In 3 years, there will be 162 bulbs in the garden.
By what factor will the number of bulbs be multiplied each year?
$ A.\:\: 1.125 \\[3ex] B.\:\: 1.5 \\[3ex] C.\:\: 3.375 \\[3ex] D.\:\: 4.85 \\[3ex] E.\:\: 38 \\[3ex] $
$ Based\:\:on\:\:the\:\:information: \\[3ex] 1st\:\:term = a = 48 \\[3ex] Increase\:\:each\:\:year\:\:until\:\:there\:\:are\:\:162\:\:bulbs\:\:in\:\:3\:\:years \\[3ex] GS:\:\:48,...,...,...,162 \\[3ex] 4th\:\:term = 162 \\[3ex] find\:\:r \\[3ex] GS_n = ar^{n - 1} \\[3ex] GS_4 = 48 * r^{4 - 1} \\[3ex] 162 = 48 * r^3 \\[3ex] 48 * r^3 = 162 \\[3ex] r^3 = \dfrac{162}{48} \\[5ex] r^3 = 3.375 \\[3ex] r = \sqrt[3]{3.375} \\[3ex] r = 1.5 \\[3ex] 2nd\:\:term = 48(1.5) = 72 \\[3ex] 3rd\:\:term = 72(1.5) = 108 \\[3ex] 4th\:\:term = 108(1.5) = 162...confirmed \\[3ex] $ The common ratio is $1.5$
This implies that each term needs to be multiplied by $1.5$ to get the subseqeunt term.