In high school, focusing on math is essential if you want to excel as an engineer. Focus on trigonometry and geometry. Study pre-calculus and calculus. You need to study algebra, and continue to do so at university level. Advanced calculus is studied at university level as are partial differential equations. The ability in theoretical math will help you throughout your career as an engineer.
Studying physics is essential in applying how mechanics and material physics principles translate into engineering. In fact, engineering is mostly about applied physics. Learning physics at high school will teach you useful verbal skills, as students are required to read paragraphs of information and develop strategies to solve the problems. Math skills like geometry and algebra are also involved in high-school-level physics. More specialized learning at university level in how physics relates to engineering can involve nanotechnology, optics, aerodynamics, control theory or solid-state physics.
Chemistry is the study of what substances are made of and how they interact with each other and what role they play in living things. Study basic and advanced chemistry in high school. At university level, chemical engineering will teach you how to carry out chemical reactions on a larger scale, and will specialize in subjects like the separation of matter, and the flow of heat and matter.
In the last years of university, you will study courses in engineering. For example, in mechanical engineering you will learn fluid mechanics, solid mechanics, heat transfer, vibrations, stress analysis and thermodynamics. A design course will often be included in the curriculum alongside a computer or laboratory class, so be prepared to study these subjects well if you want to excel in your engineering degree.