Daily Practice · Higher Plus
November 1991 - Higher Plus 5-a-day
Printing for a group?
The batch download puts all 5 tiers' November 1991 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in November 1991
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st November 1991The probability of winning a game is 3/4. A player expects 36 wins. How many games did they play?
- 2nd November 1991On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 3rd November 1991x = 40 and y = 18, each correct to the nearest whole number. Work out the upper bound of x - y.
- 4th November 1991Prove that the sum of 9 consecutive integers is always a multiple of 9. State the simplified sum you would use.
- 5th November 1991y is directly proportional to x^3. When x = 2, y = 16. Work out y when x = 3.
- 6th November 1991In a vector proof you find that vector PQ = a + b and vector RS = 5a + 5b. What does this show about PQ and RS?
- 7th November 1991A bag holds 4 red and n blue counters. The probability of taking a red is 2/5. Work out n.
- 8th November 1991A histogram has two bars: one 5 units wide with frequency density 1.5, one 25 units wide with density 1.4. How many values in total?
- 9th November 1991A car covers 860 m (to the nearest 10 m) in 9 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 10th November 1991f(x) = 5x - 5 and g(x) = 5x - 7. Work out fg(-3).
- 11th November 1991y is directly proportional to sqrt(x). When x = 49, y = 14. Work out y when x = 64.
- 12th November 1991A cuboid measures 7 cm by 6 cm by 4 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 13th November 1991A bag holds 4 red and 4 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 14th November 1991On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 15th November 1991Rationalise the denominator of 50/sqrt(5), giving your answer in its simplest form.
- 16th November 1991The curve y = cos x° is drawn for 0 <= x <= 360. Write down the value of y when x = 270.
- 17th November 1991A train slows steadily from 36 m/s to rest in 8 seconds. Work out its deceleration.
- 18th November 1991A cuboid measures 6 cm by 14 cm by 9 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 19th November 1991A bag holds 4 red, 7 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 20th November 1991A histogram has two bars: one 5 units wide with frequency density 1.2, one 10 units wide with density 1.4. How many values in total?
- 21st November 1991Simplify sqrt(80) + sqrt(245), giving your answer in the form a sqrt(b).
- 22nd November 1991A quadratic sequence starts 11, 27, 53, 89. Work out the second difference, and the coefficient of n^2.
- 23rd November 1991y is inversely proportional to x^2. When x = 2, y = 25. Work out y when x = 5.
- 24th November 1991The point (8, 15) lies on the circle x^2 + y^2 = 289. Work out the gradient of the tangent to the circle at that point.
- 25th November 1991A bag holds 8 counters, r of them red. Two are taken without replacement and P(both red) = 1/28. Work out r.
- 26th November 1991On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 27th November 1991A rectangle is 5 cm by 13 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 28th November 1991Solve x^2 - 8x + 7 < 0.
- 29th November 1991y is directly proportional to x^3. When x = 4, y = 256. Work out y when x = 2.
- 30th November 1991In a circle theorem proof, a step uses the fact that the alternate segment theorem is being proved. State the reason being quoted.