Daily Practice · Higher Plus
October 1993 - Higher Plus 5-a-day
Printing for a group?
The batch download puts all 5 tiers' October 1993 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in October 1993
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st October 1993y is directly proportional to x^3. When x = 4, y = 192. Work out y when x = 3.
- 2nd October 1993A cuboid measures 12 cm by 3 cm by 5 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 3rd October 1993A bag holds 6 red and 4 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 4th October 1993A histogram has two bars: one 5 units wide with frequency density 2, one 10 units wide with density 0.8. How many values in total?
- 5th October 1993Expand and simplify (6 + sqrt(11))(6 - sqrt(11)).
- 6th October 1993Work out the nth term of the quadratic sequence 0, 11, 28, 51, ...
- 7th October 1993y is directly proportional to sqrt(x). When x = 16, y = 32. Work out y when x = 4.
- 8th October 1993A cuboid measures 13 cm by 10 cm by 4 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 9th October 1993A bag holds 3 red, 6 blue and 4 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 10th October 1993On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 11th October 1993A block has mass 880 g (to the nearest 10 g) and volume 8 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 12th October 1993The point (-4, 0) lies on y = f(x). Write down its image on y = f(x) - 3.
- 13th October 1993A train slows steadily from 19 m/s to rest in 4 seconds. Work out its deceleration.
- 14th October 1993The point (12, 16) lies on the circle x^2 + y^2 = 400. Work out the gradient of the tangent to the circle at that point.
- 15th October 1993A bag holds 5 counters, r of them red. Two are taken without replacement and P(both red) = 3/10. Work out r.
- 16th October 1993A histogram has two bars: one 5 units wide with frequency density 2.5, one 10 units wide with density 3.5. How many values in total?
- 17th October 1993x = 81 and y = 17, each correct to the nearest whole number. Work out the upper bound of x - y.
- 18th October 1993Prove that the sum of 5 consecutive integers is always a multiple of 5. State the simplified sum you would use.
- 19th October 1993y is inversely proportional to x^2. When x = 5, y = 36. Work out y when x = 6.
- 20th October 1993In a circle theorem proof, a step uses the fact that the angle in a semicircle is being proved. State the reason being quoted.
- 21st October 1993The probability of winning a game is 3/8. A player expects 18 wins. How many games did they play?
- 22nd October 1993On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 23rd October 1993A car covers 480 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.
- 24th October 1993f(x) = 2x - 8 and g(x) = 2x - 9. Work out fg(6).
- 25th October 1993y is directly proportional to x^3. When x = 3, y = 54. Work out y when x = 2.
- 26th October 1993In a vector proof you find that vector PQ = 2a - 2b and vector RS = 8a - 8b. What does this show about PQ and RS?
- 27th October 1993A bag holds 2 red and n blue counters. The probability of taking a red is 1/3. Work out n.
- 28th October 1993A histogram has two bars: one 20 units wide with frequency density 1.5, one 5 units wide with density 0.8. How many values in total?
- 29th October 1993Rationalise the denominator of 40/sqrt(5), giving your answer in its simplest form.
- 30th October 1993The curve y = cos x° is drawn for 0 <= x <= 360. Write down the value of y when x = 180.
- 31st October 1993y is directly proportional to sqrt(x). When x = 4, y = 4. Work out y when x = 81.