Daily Practice · Higher Plus
July 1993 - Higher Plus 5-a-day
Printing for a group?
The batch download puts all 5 tiers' July 1993 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in July 1993
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st July 1993Simplify sqrt(32) + sqrt(8), giving your answer in the form a sqrt(b).
- 2nd July 1993The point (4, -3) lies on y = f(x). Write down its image on y = f(-x).
- 3rd July 1993y is directly proportional to sqrt(x). When x = 16, y = 36. Work out y when x = 25.
- 4th July 1993A cuboid measures 14 cm by 12 cm by 9 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 5th July 1993A 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?
- 6th July 1993On 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?
- 7th July 1993A rectangle is 29 cm by 20 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 8th July 1993Prove that the sum of 7 consecutive integers is always a multiple of 7. State the simplified sum you would use.
- 9th July 1993A train slows steadily from 14 m/s to rest in 5 seconds. Work out its deceleration.
- 10th July 1993A cuboid measures 4 cm by 5 cm by 11 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 11th July 1993A bag holds 5 red, 6 blue and 6 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 12th July 1993A histogram has two bars: one 5 units wide with frequency density 1.5, one 5 units wide with density 3. How many values in total?
- 13th July 1993Expand and simplify (4 + sqrt(6))(4 - sqrt(6)).
- 14th July 1993f(x) = 3x - 2 and g(x) = 2x - 8. Work out fg(4).
- 15th July 1993y is inversely proportional to x^2. When x = 2, y = 32. Work out y when x = 4.
- 16th July 1993The point (6, 8) lies on the circle x^2 + y^2 = 100. Work out the gradient of the tangent to the circle at that point.
- 17th July 1993A bag holds 5 counters, r of them red. Two are taken without replacement and P(both red) = 1/10. Work out r.
- 18th July 1993On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 19th July 1993A block has mass 610 g (to the nearest 10 g) and volume 22 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 20th July 1993The curve y = sin x° is drawn for 0 <= x <= 360. Write down the value of y when x = 0.
- 21st July 1993y is directly proportional to x^3. When x = 4, y = 256. Work out y when x = 3.
- 22nd July 1993In a circle theorem proof, a step uses the fact that the alternate segment theorem is being proved. State the reason being quoted.
- 23rd July 1993The probability of winning a game is 1/4. A player expects 5 wins. How many games did they play?
- 24th July 1993A histogram has two bars: one 20 units wide with frequency density 2, one 5 units wide with density 0.6. How many values in total?
- 25th July 1993x = 95 and y = 81, each correct to the nearest whole number. Work out the upper bound of x - y.
- 26th July 1993A quadratic sequence starts 4, 9, 20, 37. Work out the second difference, and the coefficient of n^2.
- 27th July 1993y is directly proportional to sqrt(x). When x = 4, y = 10. Work out y when x = 49.
- 28th July 1993In a vector proof you find that vector PQ = 5a + 5b and vector RS = 10a + 10b. What does this show about PQ and RS?
- 29th July 1993A bag holds 6 red and n blue counters. The probability of taking a red is 3/5. Work out n.
- 30th July 1993On 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?
- 31st July 1993A car covers 630 m (to the nearest 10 m) in 7 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.