Daily Practice · Higher Plus
October 1996 - Higher Plus 5-a-day
Printing for a group?
The batch download puts all 5 tiers' October 1996 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in October 1996
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st October 1996Expand and simplify (2 + sqrt(6))(2 - sqrt(6)).
- 2nd October 1996Write 5/(x - 2) + 7/(x + 6) as a single fraction.
- 3rd October 1996y is inversely proportional to x^2. When x = 2, y = 18. Work out y when x = 3.
- 4th October 1996In a circle theorem proof, a step uses the fact that the three angles of triangle OAB are being summed. State the reason being quoted.
- 5th October 1996The probability of winning a game is 5/8. A player expects 40 wins. How many games did they play?
- 6th October 1996On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 7th October 1996A block has mass 690 g (to the nearest 10 g) and volume 21 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 8th October 1996Solve 12x^2 + 7x - 12 = 0.
- 9th October 1996y is directly proportional to x^3. When x = 3, y = 162. Work out y when x = 4.
- 10th October 1996In a vector proof you find that vector PQ = 6a + b and vector RS = 30a + 5b. What does this show about PQ and RS?
- 11th October 1996A bag holds 3 red and n blue counters. The probability of taking a red is 3/5. Work out n.
- 12th October 1996A histogram has two bars: one 10 units wide with frequency density 1.5, one 25 units wide with density 3.5. How many values in total?
- 13th October 1996x = 199 and y = 188, each correct to the nearest whole number. Work out the upper bound of x - y.
- 14th October 1996f(x) = 5x + 9. Work out the inverse function f^-1(x).
- 15th October 1996y is directly proportional to sqrt(x). When x = 25, y = 10. Work out y when x = 16.
- 16th October 1996A cuboid measures 6 cm by 14 cm by 13 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 17th October 1996A bag holds 6 red and 5 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 18th October 1996On a histogram, a 10-wide bar and a 20-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 19th October 1996A car covers 320 m (to the nearest 10 m) in 2 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 20th October 1996Solve x^2 + y^2 = 225 and y = x + 3 simultaneously.
- 21st October 1996A train slows steadily from 32 m/s to rest in 4 seconds. Work out its deceleration.
- 22nd October 1996A cuboid measures 13 cm by 10 cm by 11 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 23rd October 1996A bag holds 3 red, 4 blue and 2 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 24th October 1996A histogram has two bars: one 20 units wide with frequency density 2.5, one 5 units wide with density 3.5. How many values in total?
- 25th October 1996Rationalise the denominator of 14/sqrt(7), giving your answer in its simplest form.
- 26th October 1996Use the iteration x(n+1) = cube root of (6x(n) + 9) with x(0) = 1. Work out x(1) to 3 decimal places.
- 27th October 1996y is inversely proportional to x^2. When x = 3, y = 25. Work out y when x = 5.
- 28th October 1996The point (9, 12) lies on the circle x^2 + y^2 = 225. Work out the gradient of the tangent to the circle at that point.
- 29th October 1996A bag holds 11 counters, r of them red. Two are taken without replacement and P(both red) = 2/11. Work out r.
- 30th October 1996On a histogram, a 5-wide bar and a 10-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 31st October 1996Simplify sqrt(32) + sqrt(50), giving your answer in the form a sqrt(b).