Daily Practice · Higher Plus
August 1993 - Higher Plus 5-a-day
Printing for a group?
The batch download puts all 5 tiers' August 1993 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in August 1993
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st August 1993Solve x^2 - 3x + 2 > 0.
- 2nd August 1993A train slows steadily from 13 m/s to rest in 5 seconds. Work out its deceleration.
- 3rd August 1993A cuboid measures 6 cm by 12 cm by 9 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 4th August 1993A bag holds 6 red and 6 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 5th August 1993A histogram has two bars: one 20 units wide with frequency density 2.5, one 5 units wide with density 3. How many values in total?
- 6th August 1993Rationalise the denominator of 60/sqrt(5), giving your answer in its simplest form.
- 7th August 1993Write x^2 + 16x - 10 in the form (x + a)^2 + b.
- 8th August 1993y is inversely proportional to x^2. When x = 4, y = 144. Work out y when x = 6.
- 9th August 1993A cuboid measures 8 cm by 6 cm by 10 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 10th August 1993A bag holds 6 red, 5 blue and 2 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 11th August 1993On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 12th August 1993Simplify sqrt(75) + sqrt(147), giving your answer in the form a sqrt(b).
- 13th August 1993Work out the coordinates of the turning point of y = x^2 + 2x - 7.
- 14th August 1993y is directly proportional to x^3. When x = 4, y = 192. Work out y when x = 3.
- 15th August 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.
- 16th August 1993A bag holds 9 counters, r of them red. Two are taken without replacement and P(both red) = 1/6. Work out r.
- 17th August 1993A histogram has two bars: one 5 units wide with frequency density 1.5, one 10 units wide with density 3.5. How many values in total?
- 18th August 1993A rectangle is 25 cm by 20 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 19th August 1993Simplify (x^2 + 2x - 15)/(x + 5).
- 20th August 1993y is directly proportional to sqrt(x). When x = 9, y = 18. Work out y when x = 64.
- 21st August 1993In a circle theorem proof, a step uses the fact that a tangent meets a radius at the point of contact. State the reason being quoted.
- 22nd August 1993The probability of winning a game is 7/10. A player expects 91 wins. How many games did they play?
- 23rd August 1993On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 24th August 1993Expand and simplify (3 + sqrt(2))(3 - sqrt(2)).
- 25th August 1993In an algebraic proof, how would you write three consecutive integers in terms of an integer n?
- 26th August 1993A train slows steadily from 24 m/s to rest in 5 seconds. Work out its deceleration.
- 27th August 1993In a vector proof you find that vector PQ = 2a + 5b and vector RS = 6a + 15b. What does this show about PQ and RS?
- 28th August 1993A bag holds 2 red and n blue counters. The probability of taking a red is 2/9. Work out n.
- 29th August 1993A histogram has two bars: one 5 units wide with frequency density 1.5, one 10 units wide with density 3.5. How many values in total?
- 30th August 1993A block has mass 510 g (to the nearest 10 g) and volume 15 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 31st August 1993Make x the subject of 8x + 3 = y(x + 3).