UniGeniusHigher Applications of Maths

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Higher Applications of Maths

Higher Applications of Maths practice questions by section

Original questions for every section, with worked answers, and paper-style questions where each answer you type is checked.

Quick checksMultiple choice, worked or timed
Paper-style questionsTwo for every section, with software output to read
AnswersChecked in any equivalent form, then the full working

Try 4 questions

Question 1Calculator or spreadsheet
Rainfall in cells B2 to B11, in mm: 12, 25, 31, 8, 27, 25, 40, 19, 26, 3.
CellRainfall (mm)
B212
B325
B431
B58
B627
B725
B840
B919
B1026
B113
Cells B2 to B11 of a spreadsheet hold the rainfall, in mm, on ten days. What value does the formula =COUNTIF(B2:B11,">25") return?
Question 2Calculator or spreadsheet
Ana takes a bus to her Saturday job. The probability that the bus is late is 0.20.2. When the bus is late, the probability that she misses the start of her shift is 0.70.7; when it is on time, the probability is 0.10.1. The tree diagram shows this. Find the probability that Ana misses the start of her shift on a given Saturday.
Question 3Calculator or spreadsheet
A line graph of quarterly sales in thousands of pounds over three years. Year 1: 40.5, 72.0, 63.5, 48.0. Year 2: 45.5, 79.0, 66.5, 54.0. Year 3: 50.5, 86.0, 75.5, 60.0. Sales peak in Quarter 2 each year and are lowest in Quarter 1, with an upward trend.Sales (thousand pounds). Y1 Q1: Sales (thousand pounds) 40.5; Y1 Q2: Sales (thousand pounds) 72; Y1 Q3: Sales (thousand pounds) 63.5; Y1 Q4: Sales (thousand pounds) 48; Y2 Q1: Sales (thousand pounds) 45.5; Y2 Q2: Sales (thousand pounds) 79; Y2 Q3: Sales (thousand pounds) 66.5; Y2 Q4: Sales (thousand pounds) 54; Y3 Q1: Sales (thousand pounds) 50.5; Y3 Q2: Sales (thousand pounds) 86; Y3 Q3: Sales (thousand pounds) 75.5; Y3 Q4: Sales (thousand pounds) 60Sales (thousand pounds)020406080100Y1 Q1Y1 Q2Y1 Q3Y1 Q4Y2 Q1Y2 Q2Y2 Q3Y2 Q4Y3 Q1Y3 Q2Y3 Q3Y3 Q440.57263.54845.57966.55450.58675.560Sales (thousand pounds)Year and quarter
Chart values
CategorySales (thousand pounds)
Y1 Q140.5
Y1 Q272
Y1 Q363.5
Y1 Q448
Y2 Q145.5
Y2 Q279
Y2 Q366.5
Y2 Q454
Y3 Q150.5
Y3 Q286
Y3 Q375.5
Y3 Q460
The line graph shows a garden centre's sales, in thousands of pounds, for each quarter of three years. Quarter 1 of year 1 is  . Software fitted the trend line  . The mean seasonal deviations (actual sales minus trend) are: Quarter 1: −14-14, Quarter 2: +18+18, Quarter 3: +6+6, Quarter 4: −10-10. Forecast the sales for Quarter 2 of year 4.
Question 4Calculator or spreadsheet
Profit in pounds for an outdoor craft fair. Dry weather, probability 0.5: 3800 with the marquee, 5000 without. Showers, probability 0.3: 3600 with, 2500 without. Heavy rain, probability 0.2: 3000 with, a loss of 1000 without.
WeatherProbabilityProfit with marquee (pounds)Profit without marquee (pounds)
Dry0.538005000
Showers0.336002500
Heavy rain0.23000−1000
An outdoor craft fair can hire a marquee. The table shows the profit in pounds for each kind of weather, with and without the marquee, and the probability of each kind of weather. On expected value, which choice is better?

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