Daily Practice · Higher Plus
February 1999 - Higher Plus 5-a-day
Every Higher Plus sheet published in February 1999, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' February 1999 sheets in a single PDF, each tier behind its own divider page - 140 sheets in one file.
Every sheet in February 1999
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st February 1999The point (-1, 4) lies on y = f(x). Write down its image on y = f(x) + 5.
- 2nd February 1999y is directly proportional to sqrt(x). When x = 4, y = 16. Work out y when x = 36.
- 3rd February 1999A cuboid measures 10 cm by 7 cm by 11 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 4th February 1999A bag holds 8 red and 6 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 5th February 1999On a histogram, a 10-wide bar and a 20-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 6th February 1999A car covers 190 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.
- 7th February 1999Prove that the sum of 3 consecutive integers is always a multiple of 3. State the simplified sum you would use.
- 8th February 1999A train slows steadily from 24 m/s to rest in 10 seconds. Work out its deceleration.
- 9th February 1999A cuboid measures 4 cm by 12 cm by 12 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 10th February 1999A bag holds 5 red, 5 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 11th February 1999A histogram has two bars: one 5 units wide with frequency density 2, one 25 units wide with density 3. How many values in total?
- 12th February 1999Rationalise the denominator of 12/sqrt(3), giving your answer in its simplest form.
- 13th February 1999f(x) = 4x + 7 and g(x) = 4x + 5. Work out fg(3).
- 14th February 1999y is inversely proportional to x^2. When x = 5, y = 108. Work out y when x = 6.
- 15th February 1999The point (8, 15) lies on the circle x^2 + y^2 = 289. Work out the gradient of the tangent to the circle at that point.
- 16th February 1999A bag holds 12 counters, r of them red. Two are taken without replacement and P(both red) = 1/66. Work out r.
- 17th February 1999On 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?
- 18th February 1999Simplify sqrt(18) + sqrt(72), giving your answer in the form a sqrt(b).
- 19th February 1999The curve y = sin x° is drawn for 0 <= x <= 360. Write down the value of y when x = 360.
- 20th February 1999y is directly proportional to x^3. When x = 2, y = 24. Work out y when x = 3.
- 21st February 1999In 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 February 1999The probability of winning a game is 3/4. A player expects 24 wins. How many games did they play?
- 23rd February 1999A histogram has two bars: one 5 units wide with frequency density 2.5, one 5 units wide with density 0.6. How many values in total?
- 24th February 1999A rectangle is 19 cm by 20 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 25th February 1999A quadratic sequence starts 13, 27, 49, 79. Work out the second difference, and the coefficient of n^2.
- 26th February 1999y is directly proportional to sqrt(x). When x = 25, y = 45. Work out y when x = 16.
- 27th February 1999In a vector proof you find that vector PQ = 6a + 5b and vector RS = 30a + 25b. What does this show about PQ and RS?
- 28th February 1999A bag holds 5 red and n blue counters. The probability of taking a red is 5/9. Work out n.