Daily Practice · Higher Plus
August 1999 - Higher Plus 5-a-day
Every Higher Plus sheet published in August 1999, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' August 1999 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in August 1999
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st August 1999y is inversely proportional to x^2. When x = 3, y = 72. Work out y when x = 6.
- 2nd August 1999A cuboid measures 9 cm by 14 cm by 6 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 3rd August 1999A bag holds 6 red and 3 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 4th August 1999On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 5th August 1999Simplify sqrt(18) + sqrt(50), giving your answer in the form a sqrt(b).
- 6th August 1999Solve x^2 + y^2 = 289 and y = x + 7 simultaneously.
- 7th August 1999y is directly proportional to x^3. When x = 4, y = 384. Work out y when x = 3.
- 8th August 1999A cuboid measures 10 cm by 14 cm by 12 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 9th August 1999A bag holds 7 red, 4 blue and 2 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 10th August 1999A histogram has two bars: one 20 units wide with frequency density 1.5, one 10 units wide with density 0.6. How many values in total?
- 11th August 1999A rectangle is 14 cm by 17 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 12th August 1999Use the iteration x(n+1) = cube root of (4x(n) + 3) with x(0) = 2. Work out x(1) to 3 decimal places.
- 13th August 1999y is directly proportional to sqrt(x). When x = 49, y = 42. Work out y when x = 25.
- 14th August 1999The point (9, 40) lies on the circle x^2 + y^2 = 1681. Work out the gradient of the tangent to the circle at that point.
- 15th August 1999A bag holds 5 counters, r of them red. Two are taken without replacement and P(both red) = 1/10. Work out r.
- 16th August 1999On 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?
- 17th August 1999Expand and simplify (6 + sqrt(7))(6 - sqrt(7)).
- 18th August 1999Work out the nth term of the quadratic sequence 14, 24, 38, 56, ...
- 19th August 1999A train slows steadily from 28 m/s to rest in 5 seconds. Work out its deceleration.
- 20th August 1999In a circle theorem proof, a step uses the fact that the three angles of triangle OAB are being summed. State the reason being quoted.
- 21st August 1999The probability of winning a game is 2/5. A player expects 4 wins. How many games did they play?
- 22nd August 1999A histogram has two bars: one 20 units wide with frequency density 0.4, one 10 units wide with density 1.4. How many values in total?
- 23rd August 1999A block has mass 760 g (to the nearest 10 g) and volume 19 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 24th August 1999The point (2, 2) lies on y = f(x). Write down its image on y = -f(x).
- 25th August 1999y is inversely proportional to x^2. When x = 3, y = 108. Work out y when x = 6.
- 26th August 1999In a vector proof you find that vector PQ = 3a + 5b and vector RS = 12a + 20b. What does this show about PQ and RS?
- 27th August 1999A bag holds 3 red and n blue counters. The probability of taking a red is 1/3. Work out n.
- 28th August 1999On 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?
- 29th August 1999x = 96 and y = 75, each correct to the nearest whole number. Work out the upper bound of x - y.
- 30th August 1999Prove that the sum of 3 consecutive integers is always a multiple of 3. State the simplified sum you would use.
- 31st August 1999y is directly proportional to x^3. When x = 3, y = 81. Work out y when x = 2.